Operator Theory, Complex Analysis,
Riemann-Hilbert problems, integrable systems, applications to
Physics and Engineering.
Research papers
1. M.C.Câmara, A.B.Lebre,
F.-O.Speck: Meromorphic factorization, partial index estimates and
elastodynamic difraction problems; Math. Nachr.,157(1992),291-372. 2. M.C.Câmara, A.B.Lebre, F.-O.Speck: Generalized
factorization for a class of Jones-form matrix functions; Proc. R.
Soc. Ed.,123A(1993),401-422.
3. M.C.Câmara, A.F.dos Santos: Generalized factorization
for a class of nxn matrix functions - Partial indices and explicit
formulas; Int. Eq. Op. Th.,20(1994),198-230.
4. M.C.Câmara, A.F.dos Santos, M.A.Bastos: Generalized
factorization for Daniele-Khrapkov matrix functions - Partial
indices; J. Math. An. Appl.,190(1995),142-164.
5. M.C.Câmara, A.F.dos Santos, M.A.Bastos: Generalized
factorization for Daniele-Khrapkov matrix functions - Explicit
formulas; J. Math. An. Appl.,190(1995),295-328.
6. M.C.Câmara: Factorization in a Banach Algebra and the
Gelfand transform; Math. Nachr., 176 (1995), 17-37.
7. M.C.Câmara, A.F.dos Santos: A non-linear approach to
generalized factorization of matrix functions; Operator Theory:
Advances and Applications,Vol.102(1998),21-37.
8. M.C.Câmara, A.F.dos Santos: Wiener-Hopf factorization of
a generalized Daniele-Khrapkov class of 2x2 matrix symbols; Math.
Meth. Appl. Sci.,22(1999),461-484.
9. M.C.Câmara, A.F.dos Santos: Wiener-Hopf factorization
for a class of oscillatory symbols; Int. Eq. Op. Th.,
36(2000),409-432.
10. M.C.Câmara, M.T.Malheiro: Wiener-Hopf factorization for
a group of exponentials of nilpotent matrices; Linear Alg.
Appl.,320(2000),79-96.
11. M.C.Câmara, A.F.dos Santos, N. Mnojlovic: Generalized
factorization for NxN Daniele-Khrapkov matrix functions; Math.
Meth. Appl. Sci.,24(2001),993-1020.
12. M.C.Câmara, A.F.dos Santos, M.P.Carpentier: Explicit
Wiener-Hopf factorization and non-linear Riemann-Hilbert problems;
Proc. R. Soc. Ed.,132A(2002),45-74. 13. M.C.Câmara, M.C.Martins, A.F.dos Santos:
A new approach to factorization of a class of almost-periodic
triangular symbols and related Riemann-Hilbert problems; J. Funct.
Anal., 235(2006)559-592.
14. M.C.Câmara, M.C.Martins: Explicit almost-periodic
factorization for a class of triangular matrix functions; J. Anal.
Math.103(2007),221-260. 15. M.C.Câmara, A.F.dos Santos, P.F.dos Santos:
Lax Equations, Factorization and Riemann-Hilbert Problems;
Port. Math.(N.S.),64(2007)no. 4,509-533.
16.
M.C.Câmara, C.Diogo: Invertibility of Toeplitz operators and
corona conditions in a strip; J.
Math. Anal. Appl. 342(2008)no.2,1297-1317.
17. M.C.Câmara, M.T.Malheiro:
Meromorphic factorization revisited and application to a group
of matrices; Complex Anal. Oper. Theory 2(2008)no.2,299-326.
18. M.C.Câmara, A.F.dos Santos, Pedro F. dos Santos:
Matrix Riemann-Hilbert problems and factorization on Riemann
surfaces; J. Funct. Anal. 255(2008)no.1,228-254.
19. M.C.Câmara, Yu.I.Karlovich, I.M.Spitkovsky: Almost
periodic factorization of some triangular matrix functions;
Modern analysis and applications.The Mark Krein Centenary
Conference. Vol.1:Operator theory and related
topics,171-190,2009.
20. C.Benhida, M.C.Câmara, C.Diogo: Some properties of
the kernel and the cokernel of Toeplitz operators with matrix
symbols; Linear Algebra Appl. 432(2010)no.1,307-317.
21. M.C.Câmara,
Yu.I.Karlovich, I.M.Spitkovsky: Constructive almost periodic
factorization of some triangular matrix functions;
J. Math. Anal. Appl. 367(2010)416-433.
22. M.C.Câmara, C. Diogo, L.Rodman: Fredholmness of
Toeplitz operators and corona problems; J. Funct. Anal.
259(2010)no.5 1273-1299.
24. M.C.Câmara,
M.T.Malheiro: Factorization in a torus and Riemann-Hilbert
problems; Journal of Mathematical Analysis and Applications
386 (2012), pp. 343-363. https://arxiv.org/abs/1010.5460
25. M.C.Câmara, Yu. I. Karlovich, I. M. Spitkovsky:
Kernels of asymmetric Toeplitz operators and applications to
almost periodic factorization; Complex Anal. Oper. Theory, 7 (2013)
no.2, 375-407.
26. M.C.Câmara,
L.Rodman, I. M. Spitkovsky:
One sided invertibility over commutative rings, corona
problems, and Toeplitz operators with matrix symbols; Linear
Algebra Appl. 459 (2014), 58-82. https://arxiv.org/abs/1403.6231
27. M.C.Câmara,J.R.Partington:
Near invariance and kernels of Toeplitz operators; J. Anal.
Math.124(2014), 235-260.
29. M.C. Câmara, C. Diogo, I. M. Spitkovsky: Toeplitz
operators of finite interval type and the table method; J.
Math. Anal. Appl. 432 (2015),no. 2, 1148-1173.
30.M.Cristina
Câmara, J.R.Partington: Spectral properties of
truncated Toeplitz operators by equivalence
after extension, J. Math. Anal. and Appl., 433
(2016), 762-784. 31.
M.C.Câmara, M.T.Malheiro, and
J.R.Partington: Model spaces and Toeplitz
kernels in reflexive Hardy spaces; Operators
and Matrices, 10(2016),no. 1, 127-148. https://arxiv.org/abs/1507.05797
32.
M.C.Câmara, J.R.Partington: Finite-dimensional Toeplitz kernels
and nearly-invariant subspaces; J. Operator Theory, 75 (2016),
no.1, 75-90.
33. M.Cristina Câmara and J.R.Partington:
Asymmetric truncated Toeplitz operators and Toeplitz operators
with matrix symbol, J. Operator Theory, 77 (2017),
455-479. https://arxiv.org/abs/1504.06446
34. Cristina Câmara, Joanna Jurasik, Kamila Klis-Garlicka and Marek Ptak: Characterizations of
asymmetric truncated Toeplitz operators, Banach J. Math.
Anal., Volume 11, Number 4 (2017), 899-922. https://arxiv.org/abs/1607.03342
35. M.C.Câmara, G.L.Cardoso, T.Mohaupt and S.Nampuri: A
Riemann-Hilbert approach to rotating attractors, J. High
Energy Phys. 2017, no. 6, 123, 73 pp. https://arxiv.org/abs/1703.10366
36.M.Cristina Câmara:
Toeplitz operators and Wiener-Hopf factorisation: an
introduction, Concr. Oper. 2017; 4: 130-145. https://arxiv.org/abs/1710.11572
37.M. Cristina
Câmara and Jonathan R. Partington: Toeplitz kernels
and model spaces, The diversity and beauty of
applied operator theory, 139-153, Oper. Theory Adv.
Appl., 268, Birkhauser/Springer, Cham,
2018. https://arxiv.org/abs/1711.04511
38.M.
Cristina
Câmara and
Jonathan R.
Partington:
Multipliers
and
equivalences
between
Toeplitz
kernels, J.
Math. Anal.
Appl. 465
(2018), no. 1,
557-570. https://arxiv.org/abs/1611.08429
39.
M. Cristina Câmara,
Kamila Klis-Garlicka and Marek Ptak:Asymmetric truncated Toeplitz
operators and its characterizations by rank
two operators,RIMS
Kôkyûroku,
2073:110
(2018)
43.M.
Cristina Câmara
and
Jonathan R.
Partington: Scalar-type
kernels for block
Toeplitz operators,
J. Math. Anal. and
Appl., (2020)
doi.org/10.1016/j.jmaa.2020.124111
. https://arxiv.org/abs/1810.09789 44.M.
Cristina Câmara,
Kamila
Klis-Garlicka,
Bartosz
Lanucha
and Marek
Ptak: Conjugations
in L^2 and their
invariants, Analysis
and Mathematical
Physics, volume 10,
Article number: 22
(2020). https://arxiv.org/abs/1912.13265
45. M. C.
Câmara and W.T.
Ross: The dual of
the compressed
shift, Canadian
Mathematical
Bulletin (2020)
http://dx.doi.org/10.4153/S0008439520000260. https://arxiv.org/abs/2001.02587
46. P.
Aniceto, M. C.
Câmara, G.L. Cardoso
and M. Rosselló:
Weyl metrics and
Wiener-Hopf
factorization, J.
High Energ.
Phys.,124 (2020)
https://doi.org/10.1007/JHEP(2020)124. https://arxiv.org/abs/1910.10632 47.M.
Cristina Câmara,
Kamila
Klis-Garlicka,
Bartosz
Lanucha
and Marek
Ptak:
Invertibility,
Fredholmness
and kernels of
dual truncated
Toeplitz
operators,
Banach Journal
of
Mathematical
Analysis
(2020), to
appear.
https://arxiv.org/abs/1912.13266M.
48.Cristina
Câmara,
Kamila
Klis-Garlicka,
Bartosz
Lanucha
and Marek
Ptak:
Conjugations
in L^2(H). https://arxiv.org/abs/1912.13270
49.M.
Cristina Câmara,
M.
Teresa
Malheiro and
Jonathan R.
Partington:Kernels
of unbounded
Toeplitz
operators and
factorization
of symbols. https://arxiv.org/abs/2004.09985
50.M.
Cristina Câmara,
Kamila
Klis-Garlicka,
Bartosz
Lanucha
and Marek
Ptak:Compressions
of
multiplication
operators and
their
characterizations,
preprint.
Other
publications
M.
C. Câmara:
Generalized
factorization
and singular
integral
equations in
L_2(R),
Técnica
nº1/1990.
M. C. Câmara,
C. Diogo:
Generalized
factorization
and corona
problems,preprint
3, DMIST
Preprints,2006.
M.
C. Câmara: Toeplitz operators with 2x2 symbols
and
factorization
in a Riemannsurface;Proc.
of the 7thWorkshop
on Functional
Analysis and
its
Applications
in
MathematicalPhysics
and Optimal
Control,14-19
September
2009, Nemecka,
Slovak
Republic, p.
19-20
(editors: Igor
Bock and
Michal Zajac).
Conferences and seminars
Invited
talks:
1. Sommerfeld ’96 Workshop, Modern Mathematical Methods in
Diffraction Theory and Applications in Engineering,
Freudenstadt, Alemanha, 30 September-4 October 1996: Some
Recent Developments in the Wiener-Hopf Factorization of 2x2
Symbols.
2. Seminário do Grupo de Análise Funcional da
Universidade de Aveiro, Portugal, 22 November 2002:
Factorização de funções matriciais e problemas de
Riemann-Hilbert.
3.
Seminário do CMAT, Centro de Matemática da
Universidade do Minho, 30
September 2005:
Factorização generalizada de uma classe de
matrizes quase-periódicas.
4. Seminar of the
Department of Applied Mathematics,
University of Agriculture in Krakow,
Poland, 26
July 2007: Finite interval difference
equations, Riemann-Hilbert problems and
Wiener-Hopf factorization.
5.
International Conference on Operator Algebras and
Applications in Morocco, Marrakesh, Morocco, 14-18 April
2008: Fredholm properties of Toeplitz operators and
Riemann-Hilbert problems.
6. Seminario de espacios de
funciones analiticas y teoria de
operadores, Sevilha, Espanha, 17
June 2008:
Toeplitz operators, Riemann-Hilbert
problems and factorization.
7.
SWOT 2008 - Small Workshop on Operator Theory, Cracóvia,
Polónia , 28 June-1 July 2008: Almost periodic factorization
for a class of triangular matrix symbols.
8. IWOTA 2008 - International Workshop in Operator Theory
and its Applications, Williamsburg, Virginia, EUA, 22 - 26 July 2008:
Matrix Wiener-Hopf factorization and Riemann-Hilbert
problems In a Riemann surface.
9. Seminar on Operator
Theory, Function Theory and
Applications, Université Mohamed V,
Rabat, Morocco, 12 March 2010: On
some properties of the kernels of
Toeplitz operators.
10. 13th Workshop on Applications and Generalizations of
Complex Analysis, Aveiro, Portugal, 25 - 26 March 2011:
Toeplitz operators, matrix Wiener-Hopf factorization and
Riemann-Hilbert problems in a Riemann surface.
11. Functional
Analysis Seminar, Department
of Pure Mathematics,
University of Leeds, UK, 17
May 2011: Toeplitz operators
and Riemann-Hilbert problems.
12. Seminário do CMAT, Centro
de Matemática da Universidade
do Minho, 25 May 2011:
Toeplitz operators, matrix
Wiener-Hopf factorization and
Riemann-Hilbert problems in a
Riemann surface.
13.
IWOTA 2011 - International Workshop in Operator Theory and
its Applications, Sevilla, Spain, 3-9 Julho 2011; Special
session on Analytic Function Spaces, Riemann-Hilbert
problems and Toeplitz operators: Kernels of asymmetric
oeplitz operators and applications to almost periodic
factorization.
14. 6th European Congress of Mathematics, Krakow, Poland,
2-7 July 2012; Satellite Thematic Session on Special Classes
of Hilbert Space Operators : Kernels of asymmetric Toeplitz
operators and finite interval convolution operators in L2.
15. Conference on Operator Theory, Operator Algebras and
Applications, Oujda, Morocco, 14-19 December 2012: One sided
invertibility, corona problemas and applications to Toeplitz
operators.
16. Mathematical aspects of the physics of non self adjoint
operators, Edinburgh, UK, 11-15 March 2013: A
Riemann-Hilbert approach to Toeplitz operators and the
corona theorem.
17. Workshop on Operator Theory and Complex Analysis, Lille,
France, 27-29 May 2013: On some properties of the
kernels of Toeplitz operators.
18. Meeting on Riemann-Hilbert problems and their
applications, Reading, UK, 29-30 May 2013 : On some
properties of the kernels of Toeplitz operators.
19. Operators on Banach Spaces, Castro Urdiales, Espanha,
10-14 June 2013: A Riemann-Hilbert approach to Toeplitz
operators and the corona theorem.
20. Sz.-Nagy Centennial Conference, Szeged, Hungary, 24-28
June 2013: One-sided invertibility, corona problems and
applications to Toeplitz operators.
21. LARSyS 2013 - Robotics and Systems in Engineering and
Science, Lisboa, 4-5 July 2013: Convolution equations via
Riemann-Hilbert problems.
22. Journées d'Analyse 2013, Bordeaux, France, 9-11 October
2013: Kernels of Toeplitz operators, near invariance and
model spaces.
23. Kent Spectral Meeting, University of Kent, Canterbury,
UK, 14-17 April 2014: A Riemann-Hilbert approach to Toeplitz
operators and the corona theorem.
24.
Seminário do CMAT,
Centro de Matemática da
Universidade do Minho,
21 May 2014: A
Riemann-Hilbert approach
to some spectral
properties of Toeplitz
operators.
25. WIMCS-CIDMA Wiener-Hopf Workshop, Aveiro, Portugal,
23-24 June 2014: Maximal and minimal functions in model
spaces.
26. SWOT 2014, Krakow, Poland, 8-12 July 2014: Kernels of
Toeplitz operators, maximal functions and model spaces.
27. IWOTA 2014, Amsterdam, Netherlands, 14-18 July 2014
Special Session on Toeplitz Operators and Related Topics:
Asymmetric truncated Toeplitz operators.
28. IWOTA 2014, Amsterdam, Netherlands, 14-18 July 2014
Special Session on Operators, Matrices and Indefinite Inner
Products: Toeplitz operators, one sided invertibility of
matrices and corona problems.
29.
Seminar of the
Department of
Applied
Mathematics,
University of
Agriculture in
Krakow, Poland, 18
May 2015:
Truncated Toeplitz
operators and
their spectra.
30. Seminar of the
Department of
Applied
Mathematics,
University of
Agriculture in
Krakow, Poland, 26
June 2015:
Q-classes of
matrix functions
and Toeplitz
operators.
31. AMS-EMS-SPM International Meeting, Porto, Portugal,
10-13 June 2015, Special Session on Operator Theory and Its
Applications: Asymmetric truncated Toeplitz operators.
32. Doppler
Institute
Seminar,
Prague, Czech
Republic, 6
October 2015:
Spectral
properties of
truncated
Toeplitz
operators .
33. ACOTCA 2016, Ville-sur-Jarnioux/Lyon, France, 13-15 June
2016: Mini-course
on Wiener-Hopf factorisation and Toeplitz operators.
34. 5th Summer Workshop on Operator Theory - SWOT 2016,
Krakow, Poland, 5-9 July 2016: Asymmetric truncatd Toeplitz
and their symbols.
35. Operator Theory, Analysis and Mathematical Physics -
OTAMP 2016, Euler International Mathematical Institute, St.
Petersburg, Russia, 2-7 August 2016: Spectral properties of
truncated Toeplitz operators.
36. Mathematical aspects of the physics with
non-self-adjoint operators, CIRM, Marseille, France, 5-9
June 2017: Truncated Toeplitz operators.
37. XIV Advanced course in Operator Theory and Complex
Analysis, Instituto de Ciencias Matematicas,
Madrid, Spain, June 19 - 22, 2017:
Conjugations and asymmetric truncated Toeplitz operators.
38. Encontro com a Ciência e a Tecnologia em Portugal,
Sessão 15.Matemática, Lisboa, Portugal,3-5 July 2017: The
Riemann-Hilbert method: from Toeplitz operators to black
holes.
39. ILAS 2017: MS-23 Toeplitz matrices and Riemann-Hilbert
problems, Iowa State University, Ames, USA, July 24-28 2017: Truncated Toeplitz operators and
their spectra. 40. Colloquium of
the Mathematics Department,
Instituto Superior
Técnico-University
of Lisbon, 8 March
2018:
From
Toeplitz operators to black holes, and beyond.
41. Recent Trends
in Operator Theory and
Applications, Memphis, USA,
3-5 May 2018:
I - From Toeplitz matrices to black
holes, and beyond; II - Multipliers and
equivalences between Toeplitz kernels.
42. Operator
Theory 27,
Timisoara, Romenia,
2-6 July 2018: Scalar
type kernels for block Toeplitz operators.
43. 6th
Summer
Workshop on
Operator
Theory,
Krakow,
Poland, 9-13
July 2018: Completions
of partial operator matrices.
44. IWOTA 2018,
Shangai, China, 23-27 July
2018, Special Session on
Operator Theory on
Reproducing Kernel Hilbert
Spaces: Multipliers
and equivalences between
Toeplitz kernels.
45. EWM-
European Women
in Mathematics
General
Meeting 2018,
Linear
Operator
Theory and
Applications,
Graz, Austria,
3-7 September
2018: Multipliers
and equivalences
between Toeplitz
kernels.
46. 7th
Iberian
Mathematical
Meeting,
Harmonic and
Complex
Analysis,
Évora,
Portugal,
12-14 October
2018: Multipliers
between
Toeplitz
kernels.
47. Young
Functional
Analysts
Workshop YFAW
2019, Leeds,
UK, 3-5
April
2019:
Completions of
partial
operator
matrices.
48. Korea
Operator
Theory and its
Applications -
KOTAC 2019,
Gyeongju,
Korea, 27-29 June
2019:
Scalar
type kernels
for block
Toeplitz
operators.
49. Special
Session on
Operators on
Reproducing
Kernel Hilbert
Spaces, IWOTA
2019,Lisbon,
Portugal,
22-26 July
2019: Dual
truncated
Toeplitz
operators.
50. Factorisation
of matrix
functions: New
techniques and
applications -
Isaac Newton Institute
Workshop,
Cambridge, UK,
12-16 August
2019: A
Riemann-Hilbert
approach to Einstein
field
equations.
Other
talks at
international
conferences:
1. International Workshop on
Operator Theory and Applications - IWOTA 95, University of
Regensburg, Germany,31 July-4 August 1995:
A non-linear method for generalized factorization - applications
to Daniele-Khrapkov symbols.
2. Workshop on Operator Factorization and Applications, I.S.T.,
Lisbon, 12-13 February 1997: A
non-linear method for Wiener-Hopf factorization and application
to a class involving oscillatory functions.
3. Workshop on Operator Factorization and Applications,Faro,
Portugal, 2-3 October 1998:
Wiener-Hopf factorization for a class of oscillatory symbols.
4. IWOTA - Portugal 2000, International Workshop on Theory and
Applications, Faro, Portugal, 12-15 September 2000:
NxN Daniele - Khrapkov class: explicit Wiener-Hopf
factorization, structure of the factors and applications to
integrable systems.
5. International Conference on Factorization, Singular Operators
and Related Problems, in honour of Professor G. Litvinchuck,
Funchal, Portugal, 28 January-1 February 2002:
Factorization of Triangular Matrix Symbols. Structure of the
Factors and Riemann-Hilbert problems.
6. IWOTA 2004, Newcastle upon Tyne, UK, 12-16 July:
Polynomial almost periodic solutions for a class of oscillatory
Riemann-hilbert problems.
7. First Czech-Catalan Conference in Mathematics, Prague, Czech
Republic,27-28 May 2005:
Factorization of a class of almost-periodic triangular symbols
and related Riemann-Hilbert problems.
8. 2nd Joint Meeting of AMS, DMV, OMG at Mainz, Mainz, Germany,16-19 June
2005: A new approach to the invertibility of a
class of Wiener-Hopf operators.
9. OTFUSA 2005 - Conference on Operator Theory, Funtion Spaces
and Applications (7-9 july 2005), Aveiro, Portugal:
"Factorization in a Riemann Surfaces".
10. Spaces of holomorphic functions and their operators (5-9
June 2006), Marseille, France: "Invertibility of a class of
Toeplitz operators and corona problems".
11. The 21st International Conference on Operator Theory, (28
June-4 July 2006), Timisoara, Romenia: "Toeplitz operators,
solutions transformations and corona problems".
12. WOAT 2006 - Operator Algebras, Operator Theory and
Applications (1-5 September 2006), Lisbon, Portugal: "Toeplitz
operators and corona problems".
13. First Joint International Meeting between the AMS and the
PTM (31 July-3 August 2007), Warsaw, Poland:
"Invertibility of Toeplitz operators with analytic symbols and
corona conditions".
14. The RAEx Oxford Symposium (13-15 August 2007), Oxford, UK:
"On a class of Riemann-Hilbert problems with almost periodic
polynomial solutions".
15. École de Printemps d'Analyse Fonctionnelle de Rabat (18-23
May 2009), Rabat, Morocco:On the applications of the corona
theorem to the study of Toeplitz operators with analytic
symbols".
16. 7th ISAAC Congress (13-18 July 2009), London, UK: "On the
relations between the kernel of a Toeplitz operator and the
solutions to some associated Riemann-Hilbert problems".
17. Workshop in Functional Analysis and its Applications in
Mathematical Physics and Optimal Control (14-19 September 2009),
Nemecka, Slovakia: "Toeplitz operators with 2x2 symbols and
factorization in Riemann surfaces".
18. Operator Theory and Related Topics (31 May-4 June 2010),
Lille, France: "Fredholmness of Toeplitz Operators and corona
problems".
19. FAV 2010 - Functional Analysis Valencia (7-11 June 2010),
Valencia, Spain: On the kernels of Toeplitz Operators with
related symbols".
20. IWOTA 2010 - 21 International Workshop on Operator
Theory and its Applications (12-16 July 2010), Berlin, Germany:
Fredholm properties of Toeplitz operators and meromorphic corona
problems".
21. Summer School in Analysis (30 August-3 September 2010),
Touquet, France: "Factorization, Riemann-Hilbert problems and
the corona theorem".
22.
5th Annual Workshop of the Functional Analysis and Applications
Group, Universidade de Aveiro, Portugal, 24 May 2014: "On some
properties of the kernels of Toeplitz operators".
23.
Matrices & Operators - Workshop with Abraham Berman,
Coimbra, Portugal, 3-4 June 2014: "One sided invertibility of
matrices and Toeplitz operators".
24. Conference on Harmonic Analysis, Operator Theory and
Applications, Bordeaux, France, 1-6 Jun 2015 : "Asymmetric
truncated Toeplitz operators".
25. Operator Theory 26, Timisoara, Romenia, 27 June-2 July 2016:
"Spectral properties of a class of truncated Toeplitz
operators".
Research