Antonio G. García
Catedrático de Universidad

Universidad Carlos III de Madrid
Departamento de Matemáticas
Avenida de la Universidad, 30
28911, Leganés, Madrid.

Teléfono: 91 624 9443
FAX: +34 91 624 9129
Despacho: 2.1.D.27 (Edificio Sabatini)
Scientific Publications
Books
  1. A. G. García. A brief walk through Sampling Theory. Advances in Imaging and Electron Physics, 124:63-137, 2002.
  2. H. R. Fernández-Morales, A. G. García and G. Pérez-Villalón. Generalized sampling in L2(Rd) shift-invariant subspaces with multiple stable generators. In Multiscale Signal Analysis and Modelling, Lecture Notes in Electrical Engineering, Springer, 2013.
  3. A. G. García and M. J. Muñoz-Bouzo. Espacios de Hilbert y Análisis de Fourier: los primeros pasos (2ª edición revisada). Ed. Sanz y Torres, Madrid, 2020.
  4. A. G. García. Bases en espacios de Hilbert: teoría de muestreo y wavelets (2ª edición revisada). Ed. Sanz y Torres, Madrid, 2020.
  5. A. G. García. Sampling Theory and Reproducing Kernel Hilbert Spaces. In Handbook of Operator Theory, Daniel Alpay Editor-in-Chief, Springer, 2015.
  6. A. G. García, M. A. Hernández-Medina and  A. Ibort. Towards a quantum sampling theory: the case of finite groups. In 60 Years Alberto Ibort Fest, Classical and Quantum Physics. G. Marmo et al. Eds., Ch. 11, pp. 203--223, Springer, 2019.
  7. A. G. García. Sampling in the range of the analysis operator of a continuous frame having a unitary structure. In Operator Theory: Advances and Applications 285. F. Gesztesy and A. Martínez- Finkelshtein Eds., Ch. 7, pp. 91--111, Springer 2021.
              
Preprints

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Papers
  1. A. G. García. Sampling in Lambda-shift-invariant subspaces of Hilbert-Schmidt operators on L2(Rd). Math. Found. of Computing, 4(4):281--297, 2021. 
  2. A. G. García. Average sampling in certain subspaces of Hilbert-Schmidt operators on L2(Rd).  Samp. Theory Signal Process. Data Anal., 19:10, 2021.                                 
  3. A. G. García and M. J. Muñoz-Bouzo. A note on continuous stable sampling. Adv. Oper. Theory,  5(3): 994--1013,  2020.
  4. A. G. García, M. A. Hernández-Medina and G. Pérez-Villalón. Convolution systems on discrete abelian groups as a unifying strategy in sampling theory. Results Math., 75(1), 40, 2020.
  5. A. G. García, M. J. Muñoz-Bouzo and G. Pérez-Villalón. On regular generalized sampling in T-invariant subespaces of a Hilbert space: an overview. Numer. Funct. Anal. Optim., 41(6):685-708, 2020.
  6. A. G. García, M. A. Hernández-Medina and  A. Ibort. Knit product of finite groups and sampling. Mediterr. J. Math., 16(6), 146, 2019.
  7. A. G. García, M. A. Hernández-Medina and G. Pérez-Villalón. Sampling associated with a unitary representation of a semi-direct product of groups: a filter bank approach. Symmetry 2019, 11(4), 529.
  8. A. G. García and G. Pérez-Villalón. Riesz bases associated with regular representations of semidirect groups. Banach J. Anal. Math., 14(1): 41-62, 2020.
  9. A. G. García, M. A. Hernández-Medina and G. Pérez-Villalón. Filter Banks on Discrete Abelian Groups. Int. J. Wavelets Multiresolut. Inf. Process., Vol. 16, No. 3 (2018) 1850029 (20 pages).
  10. A. G. García and M. J. Muñoz-Bouzo. Sampling formulas involving differences in shift-invariant subspaces: a unified approach. Numer. Funct. Anal. Optim., 39(6):677--688, 2018.
  11. A. G. García, M. A. Hernández-Medina and G. Pérez-Villalón. Sampling in unitary invariant subspaces associated to LCA groups. Result. Math., 72:1725--1745, 2017.
  12. A. G. García,  A. Ibort and M. J. Muñoz-Bouzo. Modeling sampling in tensor products of unitary invariant subspaces. J. Funct. Spaces. Article ID 4573940, Vol. 2016, 15pp., 2016.
  13. H. R. Fernández-Morales, A. G. García,  M. J. Muñoz-Bouzo and A. Ortega. Finite sampling in multiple generated U-invariant subspaces. IEEE Trans. Inform. Theory. Vol. 62(4):2203--2212, April 2016.
  14. A. G. García and M. J. Muñoz-Bouzo. Sampling-related frames in finite U-invariant subspaces. Appl. Comput. Harmon. Anal., 39:173-184, 2015.
  15. H. R. Fernández-Morales, A. G. García,  M. A. Hernández-Medina and M. J. Muñoz-Bouzo. Generalized sampling: from shift-invariant to U-invariant spaces. Anal. Appl., Vol.13(3):303--329, 2015.
  16. A. G. García and M. A. Hernández-Medina. The zero-removing property in Hilbert spaces of entire functions arising in sampling theory.  Result. Math., 67(3-4): 471--494, 2015.
  17. A. G. García,  M. A. Hernández-Medina and A. Portal. Hyperciclity of translation operators in a reproducing kernel Hilbert space of entire functions induced by an analytic Hilbert-space-valued kernel. Osaka J. Math., 52(3), 17 pp.,  2015.
  18. A. G. García,  M. A. Hernández-Medina and M. J. Muñoz-Bouzo. The Kramer sampling theorem revisited. Acta Appl. Math., 133(1):87--111, 2014.
  19. H. R. Fernández-Morales, A. G. García,  M. A. Hernández-Medina and M. J. Muñoz-Bouzo. On some sampling-related frames in U-invariant spaces. Abstr. Appl. Anal., Vol. 2013, Article ID 761620, 14 pp., 2013.
  20. P. E. Fernández-Moncada, A. G. García and M. A. Hernández-Medina. Sampling associated with resolvent-type kernels and Lagrange-type interpolation series.  Houston J. Math., 39(4):1333--1347, 2013.
  21. A. G. García, M. A. Hernández-Medina and F. H. Szafraniec.  Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces Complex Var. Elliptic Equ.,  58(1):79--97, 2013. 
  22. A. G. García and A. Portal. Sampling in reproducing kernel Banach spaces. Mediterr. J. Math., 3(10):1399--1415, 2013.
  23. A. G. García, J. M. Kim, K. H. Kwon and G. J. Yoon. Multi-channel sampling on shift-invariant spaces with frame generators  Int. J. Wavelets Multiresolut. Inf. Process., 10(1):41-60, 2012.
  24. A. G. García, M. J. Muñoz-Bouzo and G. Pérez-Villalón. Regular multivariate sampling and approximation in Lp shift-invariant spaces. J Math. Anal. Appl., 380:607--627, 2011.
  25. A. G. García, M. A. Hernández-Medina, G. Pérez-Villalón and A. Portal. A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling. Linear Alg. Appl., 435:2837-2859, 2011.
  26. P. E. Fernández-Moncada, A. G. García and M. A. Hernández-Medina. The zero-removing property and Lagrange-type interpolation series. Numer. Funct. Anal. Optim., 32(8):858-876, 2011.
  27. A. G. García, M. A. Hernández-Medina and G. Pérez-Villalón. Oversampling in shift-invariant spaces with a rational sampling period. IEEE Trans. Signal Process., 57(9), 3442-3449, 2009.
  28. A.G. García, M.A. Hernández-Medina and G. Pérez-Villalón,  Oversampling and reconstruction functions with compact support, J. Comp. Appl. Math., 227:245--253, 2009.
  29. A.G. García and G.G. Pérez-Villalón, Multivariate generalized sampling in shift-invariant spaces and its approximation properties, J. Math. Anal. Appl., 355:397--413, 2009.
  30.  A. G. García. El uso de bases y frames en teoría de muestreo. Gaceta de la RSME, 12(2):301-314, 2009.
  31.  A. G. García and G. Pérez-Villalón. Approximation from shift-invariant spaces by generalized sampling formulas. Appl. Comput. Harmon. Anal., 24:58-69, 2008.
  32. A. G. García, M. A. Hernández-Medina and G. Pérez-Villalón. Generalized sampling in shift-invariant spaces with multiple stable generators. J. Math. Anal. Appl., 337:69-84, 2008.
  33. W. N. Everitt, A. G. García and M. A. Hernández-Medina. On Lagrange-type interpolation series and analytic Kramer kernels. Result. Math., 51(3-4):215-228, 2008.
  34. A. G. García, J. M. Kim, K. H. Kwon and G. Pérez-Villalón. Aliasing error of sampling series in wavelet subspaces. Numer. Funct. Anal. Optim., 29(1-2):126-144, 2008.
  35. A. G. García and A. Portal. A general sampling theory in the functional Hilbert space induced by a Hilbert space valued kernel. J. Appl. Funct. Anal., 3(3):299-313, 2008.
  36. A. G. García and G. Pérez-Villalón. Generalized irregular sampling in shift-invariant spaces. Int. J. Wavelets Multiresolut. Inf. Process., 5(3):369-387, 2007.
  37. A. G. García and G. Pérez-Villalón. On the truncation error of generalized sampling expansions in shift-invariant spaces. Samp. Theory Signal Image Process., 6(1):53-69, 2007.
  38.  A. G. García, M. A. Hernández-Medina and A. Portal. An approximation property of the functions defined through a resolvent sampling kernel. Far East J. Math. Sci., 26(1):65-90, 2007.
  39. A. G. García and G. Pérez-Villalón. Regular sampling in wavelet subspaces involving two sequences of sampling points. J. Comp. Anal. Appl., 9(2):131-138, 2007.
  40.  A. G. García and G. Pérez-Villalón. Dual frames in L2(0,1) connected with generalized sampling in shift-invariant spaces. Appl. Comput. Harmon. Anal., 20:422-433, 2006.
  41. A. G. García and G. Pérez-Villalón. On the aliasing error in wavelet subspaces. J, Comp. Appl. Math., 183:153-167, 2005.
  42. A. G. García, G. Pérez-Villalón and A. Portal. Riesz bases in L2(0,1) related to sampling in shift-invariant spaces. J. Math. Anal. Appl., 308(2):703-713, 2005.
  43.  A. G. García, M. A. Hernández-Medina and A. Portal. An estimation of the truncation error for the two-channel sampling formulas. J. Fourier Anal. Appl., 11(2):203-213, 2005.
  44. A. G. García and M. A. Hernández-Medina. Sampling theory associated with a symmetric operator with compact resolvent. Mediterr. J. Math., 2(3):345-356, 2005.
  45. A. G. García, M. J. Muñoz-Bouzo and A. Portal. Irregular sampling of generalized harmonizable processes. Stochastic Anal. Appl., 22(5):1327-1339, 2004.
  46. A. G. García and L. L. Littlejohn. On analytic sampling theory J. Comp. Appl. Math., 171:235-246, 2004.
  47.  A. G. García and A. Portal. Hypercircle inequalities and sampling theory. Appl. Anal., 82(12):1111-1125, 2003.
  48.  A. G. García and A. Portal. Sampling in the functional Hilbert space induced by a Hilbert space valued kernel. Appl. Anal., 82(12):1145-1158, 2003.
  49. A. G. García and M. A. Hernández-Medina. Discrete Sturm-Liouville problems, Jacobi matrices and Lagrange interpolation series. J. Math. Anal. Appl., 280(2):221-231, 2003.
  50.  A. G. García and M. A. Hernández-Medina. New results in sampling associated with difference operators. Int. Math. J., 2(6):577-593, 2002.
  51. A. G. García and F. H. Szafraniec. A converse of the Kramer sampling theorem. Samp. Theory Signal Image Process., 1(1):53-61, 2002.
  52.  A. G. García and M. A. Hernández-Medina. On the Sturm-Liouville transform: The regular case. Integr. Transf. Spec. Funct., 11(2):163-176, 2001.
  53.  A. G. García, M. A. Hernández-Medina and M. J. Muñoz-Bouzo. On the analytic form of the discrete Kramer sampling theorem. Internat. J. Math. Math. Sci., 25(11):709-715, 2001.
  54. A. G. García and M. A. Hernández-Medina. On an integral transform associated with the regular Dirac operator. Proc. Roy. Soc. Edinb., 131A:1357-1370, 2001.
  55. A. G. García and M. A. Hernández-Medina. The discrete Kramer sampling theorem and indeterminate moment problems. J. Comp. Appl. Math., 134(1-2):13-22, 2001.
  56. A. G. García. Orthogonal sampling formulas: a unified approach. SIAM Rev., 4283):499-512, 2000.
  57. A. G. García and M. A. Hernández-Medina. Sampling theorems and difference Sturm-Liouville problems. J. Difference Equ. Appl. , 6:695-717, 2000.
  58. A. G. García and M. A. Hernández-Medina. On the regular Sturm-Liouville ttransform. Extracta Math., 15(1):193-206, 2000.
  59. A. G. García and M. J. Muñoz-Bouzo. On sampling stationary stochastic processes. Appl.Anal., 75(1-2):73-84, 2000.
  60. A. G. García and M. A. Hernández-Medina. A general sampling theorem associated with differential operators. J. Comp. Anal. Appl., 1(2):147-161, 1999.
  61. A. Zayed and A. G. García. New sampling formulae for the fractional Fourier transform. Signal Process., 77:111-114, 1999.
  62. M. H. Annaby, A. G. García and M. A. Hernández-Medina. On sampling and second order difference equations. Analysis, 19:79-92, 1999.
  63. A. Zayed and A. G. García. Kramer's sampling theorem with discontinuous kernels. Result. Math., 34(1-2):197-206, 1998.
  64. A. G. García, M. A. Hernández-Medina and J. Moro. On the distributional Fourier Duality and its applications. J. Math. Anal. Appl., 227:43-54, 1998.
  65. A. Zayed and A. G. García. Nonuniform sampling of bandlimited signals with polynomial growth on the real axis. IEEE Trans. Inform. Theory, 43(5):1717-1721, 1997.
  66. A. Zayed and A. G. García. Sampling theorems associated with a Dirac operator and the Hartley transform. J. Math. Anal. Appl., 214:587-598, 1997.
  67. A. G. García. The Paley-Wiener-Levinson theorem revisited. Internat. J. Math. Math. Sci., 20(2):229-234, 1997.
  68. R. Álvarez-Nodarse, A. G. García and F. Marcellán. On the properties for modifications of classical orthogonal polynomials of discrete variables. J. Comp. Appl. Math., 65:3-18, 1995.
  69. A. G. García, L. Salto and F. Marcellán. A distributional study of discrete classical orthogonal polynomials. J. Comp. Appl. Math., 57:147-162, 1995.
  70. M. Arrate and A. G. García. On the existence, uniqueness and approximation of solutions of ordinary differential equations in Banach spaces. J. London Math. Soc., 27(2):121-129, 1983.
  71. A. G. García. Un teorema de unicidad para ecuaciones diferenciales abstractas. Publ. Sección Mat., UVA, 4:18-22, 1981.