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Volumn 171, Issue 1-2, 2004, Pages 39-57

Sampling in Paley-Wiener spaces associated with fractional integro-differential operators

Author keywords

Expansion in eigenfunctions; Integro differential eigenvalue problems of fractional orders; Mittag Leffler functions; Sampling theory

Indexed keywords

FUNCTIONS; HARMONIC ANALYSIS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS;

EID: 3042582603     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.01.008     Document Type: Article
Times cited : (5)

References (45)
  • 1
    • 0009626343 scopus 로고
    • Props d'une note de M. Pierre Humbert
    • Agarwal R.P. Props d'une note de M. Pierre Humbert C. R. Acad. Sci. Paris 236 1953 2031-2032
    • (1953) C. R. Acad. Sci. Paris , vol.236 , pp. 2031-2032
    • Agarwal, R.P.1
  • 2
    • 0010011823 scopus 로고    scopus 로고
    • Interpolation expansions associated with nonselfadjoint boundary value problems
    • Annaby M.H. Interpolation expansions associated with nonselfadjoint boundary value problems Comm. Appl. Anal. 3 1999 545-561
    • (1999) Comm. Appl. Anal. , vol.3 , pp. 545-561
    • Annaby, M.H.1
  • 3
    • 0038739211 scopus 로고    scopus 로고
    • On sampling theory associated with the resolvents of singular Sturm-Liouville problems
    • Annaby M.H. On sampling theory associated with the resolvents of singular Sturm-Liouville problems Proc. Amer. Math. Soc. 131 2003 1803-1812
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 1803-1812
    • Annaby, M.H.1
  • 4
    • 0036624781 scopus 로고    scopus 로고
    • On sampling associated with singular Sturm-Liouville eigenvalue problems: The limit circle case
    • Annaby M.H. Butzer P.L. On sampling associated with singular Sturm-Liouville eigenvalue problems: the limit circle case Rocky Mountain J. Math. 32 2002 443-466
    • (2002) Rocky Mountain J. Math. , vol.32 , pp. 443-466
    • Annaby, M.H.1    Butzer, P.L.2
  • 5
    • 0039925276 scopus 로고    scopus 로고
    • Sampling integro-differential transforms arising from second order differential operators
    • Annaby M.H. Freiling G. Sampling integro-differential transforms arising from second order differential operators Math. Nach. 216 2000 25-43
    • (2000) Math. Nach. , vol.216 , pp. 25-43
    • Annaby, M.H.1    Freiling, G.2
  • 6
    • 0039600588 scopus 로고    scopus 로고
    • Sampling expansions associated with Kamke problems
    • Annaby M.H. Freiling G. Sampling expansions associated with Kamke problems Math. Zeit. 234 2000 163-189
    • (2000) Math. Zeit. , vol.234 , pp. 163-189
    • Annaby, M.H.1    Freiling, G.2
  • 7
    • 0009974492 scopus 로고    scopus 로고
    • A sampling theorem associated with boundary-value problems with not necessarily simple eigenvalues
    • Annaby M.H. Hassan H.A. A sampling theorem associated with boundary-value problems with not necessarily simple eigenvalues Internat. J. Math. Math. Sci. 21 1998 571-580
    • (1998) Internat. J. Math. Math. Sci. , vol.21 , pp. 571-580
    • Annaby, M.H.1    Hassan, H.A.2
  • 8
    • 0000738719 scopus 로고    scopus 로고
    • On the use of Green's function in sampling theory
    • Annaby M.H. Zayed A.I. On the use of Green's function in sampling theory J. Integral Equations Appl. 10 1998 117-139
    • (1998) J. Integral Equations Appl. , vol.10 , pp. 117-139
    • Annaby, M.H.1    Zayed, A.I.2
  • 9
    • 0001114755 scopus 로고
    • A survey of the Whittaker-Shannon sampling theorem and some of its extensions
    • Butzer P.L. A survey of the Whittaker-Shannon sampling theorem and some of its extensions J. Math. Res. Exposition 3 1983 185-212
    • (1983) J. Math. Res. Exposition , vol.3 , pp. 185-212
    • Butzer, P.L.1
  • 10
    • 0002915692 scopus 로고    scopus 로고
    • Kramer's sampling theorem in signal analysis and its role in Mathematics
    • J.M. Blackledge (Ed.), The Institute of Mathematics and its Applications, New Series, Oxford: Clarendon Press
    • Butzer P.L. Nasri-Roudsari G. Kramer's sampling theorem in signal analysis and its role in Mathematics Blackledge J.M. Image Processing, Mathematical Methods and Applications The Institute of Mathematics and its Applications, New Series Vol. 61 1997 49-95 Clarendon Press Oxford
    • (1997) Image Processing, Mathematical Methods and Applications , vol.61 , pp. 49-95
    • Butzer, P.L.1    Nasri-Roudsari, G.2
  • 11
    • 0028443011 scopus 로고
    • Sampling theorems associated with fourth and higher order self-adjoint eigenvalue problems
    • Butzer P.L. Schöttler G. Sampling theorems associated with fourth and higher order self-adjoint eigenvalue problems J. Comput. Appl. Math. 51 1994 159-177
    • (1994) J. Comput. Appl. Math. , vol.51 , pp. 159-177
    • Butzer, P.L.1    Schöttler, G.2
  • 13
    • 0000932728 scopus 로고
    • A comparison of the sampling theorems of Kramer and Whittaker
    • Campbell L.L. A comparison of the sampling theorems of Kramer and Whittaker SIAM J. Appl. Math. 12 1964 117-130
    • (1964) SIAM J. Appl. Math. , vol.12 , pp. 117-130
    • Campbell, L.L.1
  • 17
    • 2242471442 scopus 로고    scopus 로고
    • On the representation of holomorphic functions by integrals
    • Everitt W.N. Hayman W.K. Nasri-Roudsari G. On the representation of holomorphic functions by integrals Appl. Anal. 65 1997 95-102
    • (1997) Appl. Anal. , vol.65 , pp. 95-102
    • Everitt, W.N.1    Hayman, W.K.2    Nasri-Roudsari, G.3
  • 18
    • 0002375729 scopus 로고    scopus 로고
    • Interpolation and sampling theories, and linear ordinary boundary value problems
    • J.R. Higgins, & R.L. Stens (Eds.), Oxford: Oxford University Press
    • Everitt W.N. Nasri-Roudsari G. Interpolation and sampling theories, and linear ordinary boundary value problems Higgins J.R. Stens R.L. Sampling Theory in Fourier and Signal Analysis; Advanced Topics 1999 96-129 Oxford University Press Oxford
    • (1999) Sampling Theory in Fourier and Signal Analysis; Advanced Topics , pp. 96-129
    • Everitt, W.N.1    Nasri-Roudsari, G.2
  • 19
    • 0000836713 scopus 로고    scopus 로고
    • Sturm-Liouville problems with coupled boundary conditions and Lagrange interpolation series
    • Everitt W.N. Nasri-Roudsari G. Sturm-Liouville problems with coupled boundary conditions and Lagrange interpolation series J. Comput. Anal. Appl. 1 1999 319-347
    • (1999) J. Comput. Anal. Appl. , vol.1 , pp. 319-347
    • Everitt, W.N.1    Nasri-Roudsari, G.2
  • 20
    • 0010009542 scopus 로고    scopus 로고
    • Sturm-Liouville problems with coupled boundary conditions and Lagrange interpolation series: II
    • Everitt W.N. Nasri-Roudsari G. Sturm-Liouville problems with coupled boundary conditions and Lagrange interpolation series: II Rend. di Mat. Roma 20 7 2000 199-238
    • (2000) Rend. Di Mat. Roma , vol.20 , Issue.7 , pp. 199-238
    • Everitt, W.N.1    Nasri-Roudsari, G.2
  • 21
    • 0001580347 scopus 로고    scopus 로고
    • A note on the analytic form of the Kramer sampling theorem
    • Everitt W.N. Nasri-Roudsari G. Rehberg J. A note on the analytic form of the Kramer sampling theorem Results in Math. 34 1998 310-319
    • (1998) Results in Math. , vol.34 , pp. 310-319
    • Everitt, W.N.1    Nasri-Roudsari, G.2    Rehberg, J.3
  • 22
    • 0036857725 scopus 로고    scopus 로고
    • Kramer analytic kernels and first-order boundary value problems
    • Everitt W.N. Poulkou A. Kramer analytic kernels and first-order boundary value problems J. Comput. Appl. Math. 148 2002 22-47
    • (2002) J. Comput. Appl. Math. , vol.148 , pp. 22-47
    • Everitt, W.N.1    Poulkou, A.2
  • 23
    • 0002772914 scopus 로고
    • Sturm-Liouville boundary value problems and Lagrange interpolation series
    • Everitt W.N. Schöttler G. Butzer P.L. Sturm-Liouville boundary value problems and Lagrange interpolation series Rend. di Mat. Roma 14 7 1994 87-126
    • (1994) Rend. Di Mat. Roma , vol.14 , Issue.7 , pp. 87-126
    • Everitt, W.N.1    Schöttler, G.2    Butzer, P.L.3
  • 24
    • 84968492701 scopus 로고
    • Parametrizations of Titchmarsh's m(λ)-functions in the limit circle case
    • Fulton C.T. Parametrizations of Titchmarsh's m(λ)-functions in the limit circle case Trans. Amer. Math. Soc. 229 1977 51-63
    • (1977) Trans. Amer. Math. Soc. , vol.229 , pp. 51-63
    • Fulton, C.T.1
  • 28
    • 0001233578 scopus 로고
    • On the theory of integral equations
    • Hille E. Tamarkin J. On the theory of integral equations Ann. Math. 31 1930 479-528
    • (1930) Ann. Math. , vol.31 , pp. 479-528
    • Hille, E.1    Tamarkin, J.2
  • 30
    • 0039293981 scopus 로고
    • Sur la function de Mittag-Leffler et quelques-unes de ses généralisations
    • Humbert P. Agarwal R.P. Sur la function de Mittag-Leffler et quelques-unes de ses généralisations Bull. Sci. Math. 77 1953 180-185
    • (1953) Bull. Sci. Math. , vol.77 , pp. 180-185
    • Humbert, P.1    Agarwal, R.P.2
  • 31
    • 0000701478 scopus 로고
    • The exact value of the Paley-Wiener constant
    • Kadec M.I. The exact value of the Paley-Wiener constant Sov. Math. Dokl. 5 1964 559-561
    • (1964) Sov. Math. Dokl. , vol.5 , pp. 559-561
    • Kadec, M.I.1
  • 32
    • 33747444473 scopus 로고
    • A generalized sampling theorem
    • Kramer H.P. A generalized sampling theorem J. Math. Phys. 38 1959 68-72
    • (1959) J. Math. Phys. , vol.38 , pp. 68-72
    • Kramer, H.P.1
  • 35
    • 19044384354 scopus 로고
    • Sur la représentation analytique d'une branche uniforme d'une fonction monogéne
    • Mittag-Leffler G.M. Sur la représentation analytique d'une branche uniforme d'une fonction monogéne Acta Math. 29 1905 101-182
    • (1905) Acta Math. , vol.29 , pp. 101-182
    • Mittag-Leffler, G.M.1
  • 40
    • 0009975497 scopus 로고
    • Sampling theorems associated with Sturm-Liouville systems
    • Weiss P. Sampling theorems associated with Sturm-Liouville systems Bull. Amer. Math. Soc. 163 1957 242
    • (1957) Bull. Amer. Math. Soc. , vol.163 , pp. 242
    • Weiss, P.1
  • 41
  • 43
    • 0026141901 scopus 로고
    • On Kramer's sampling theorem associated with general Sturm-Liouville problems and Lagrange interpolation
    • Zayed A.I. On Kramer's sampling theorem associated with general Sturm-Liouville problems and Lagrange interpolation SIAM J. Appl. Math. 51 1991 575-604
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 575-604
    • Zayed, A.I.1
  • 44
    • 0025449055 scopus 로고
    • On Lagrange interpolation and Kramer-type sampling theorems associated with Sturm-Liouville problems
    • Zayed A.I. Hinsen G. Butzer P.L. On Lagrange interpolation and Kramer-type sampling theorems associated with Sturm-Liouville problems SIAM J. Appl. Math. 50 1990 893-909
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 893-909
    • Zayed, A.I.1    Hinsen, G.2    Butzer, P.L.3
  • 45
    • 0002704845 scopus 로고
    • On Lagrange interpolation and Kramer's sampling theorem associated with self-adjoint boundary value problems
    • Zayed A.I. EL-Sayed M.A. Annaby M.H. On Lagrange interpolation and Kramer's sampling theorem associated with self-adjoint boundary value problems J. Math. Anal. Appl. 158 1991 269-284
    • (1991) J. Math. Anal. Appl. , vol.158 , pp. 269-284
    • Zayed, A.I.1    EL-Sayed, M.A.2    Annaby, M.H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.