Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, , 176 - 183, 15.09.2023
https://doi.org/10.33205/cma.1323956

Öz

Proje Numarası

FSE - REACT EU, PON Ricerca e Innovazione 2014-2020

Kaynakça

  • R. Balan, P.G. Casazza, C. Heil and Z. Landau: Density, overcompleteness, and localization of frames I. Theory, J. Fourier Anal. Appl., 12 (2006), 105–143.
  • P. Balazs: Basic definition and properties of Bessel multipliers, J. Math. Anal. Appl., 325 (1) (2007), 571–585.
  • P. Balazs: Hilbert-Schmidt operators and frames-classification, best approximation by multipliers and algorithms, Int. J. Wavelets Multiresolut. Inf. Process., 6 (2) (2008), 315–330.
  • P. Balazs, B. Laback, G. Eckel and W.A. Deutsch: Time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking, IEEE Transactions on Audio, Speech, and Language Processing, 18 (1) (2010), 34–49.
  • P. Balazs, D. T. Stoeva: Representation of the inverse of a frame multiplier, J. Math. Anal. Appl., 422 (2) (2015), 981–994.
  • O. Christensen: An Introduction to Frames and Riesz Bases, second expanded edition, Birkhäuser, Boston, (2016).
  • J. Conway: A Course in Functional Analysis, Graduate Texts in Mathematics. 96 (2nd ed.), New York: Springer-Verlag, (1990).
  • E. Cordero, K. Gröchenig: Localization of frames II, Appl. Comput. Harmon. Anal., 17 (2004), 29–47.
  • R. Corso: On some dual frames multipliers with at most countable spectra, Ann. Mat. Pura Appl., 201 (4) (2022), 1705–1716.
  • R. Corso: Localization of the spectra of dual frames multipliers, Constr. Math. Anal., 5 (4) (2022), 238–245.
  • R. Corso, F. Tschinke: Some notes about distribution frame multipliers, in: Landscapes of Time-Frequency Analysis, vol. 2, P. Boggiatto, T. Bruno, E. Cordero, H.G. Feichtinger, F. Nicola, A. Oliaro, A. Tabacco, M. Vallarino (Ed.), Applied and Numerical Harmonic Analysis Series, Springer, (2020).
  • H. G. Feichtinger, K. Nowak: A first survey of Gabor multipliers, in: Advances in Gabor analysis, H. G. Feichtinger and T. Strohmer (Ed.), Boston Birkhäuser, Applied and Numerical Harmonic Analysis, (2003).
  • G. B. Folland: A Course in Abstract Harmonic Analysis, CRC Press, Boca, Raton, (1995).
  • J.-P. Gazeau: Coherent States in Quantum Physics, Weinheim: Wiley, (2009).
  • K. Gröchenig: Foundations of Time-Frequency Analysis, Birkhäauser, Boston, (2000).
  • K. Gröchenig: Localization of frames, Banach frames, and the invertibility of the frame operator, J. Fourier Anal. Appl., 10 (2004), 105–132.
  • K. Gröchenig, M. Fornasier: Intrinsic localization of frames, Constr. Approx., 22 (2005), 395–415.
  • E. Hernández, H. Šiki´c, G. Weiss and E. N. Wilson: Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform, Colloq. Math., 118 (1) (2010), 313–332.
  • H. Javanshiri, M. Abolghasemi, A.A. Arefijamaal: The essence of invertible frame multipliers in scalability, Adv. Comput. Math., 48 (2022), ARTICLE ID: 19.
  • T. Kato: Perturbation Theory for Linear Operators, Springer, Berlin, (1966).
  • G. Matz, F. Hlawatsch: Linear time-frequency filters: On-line algorithms and applications, in: A. Papandreou- Suppappola (Ed.), Application in Time-Frequency Signal Processing, CRC Press, Boca Raton, FL, (2002).
  • R. Levie, H. Avron: Randomized Signal Processing with Continuous Frames, J. Fourier Anal. Appl., 28 (2022), ARTICLE ID: 5.
  • K. Schmüdgen: Unbounded Self-adjoint Operators on Hilbert Space, Springer, Dordrecht, (2012).
  • D. T. Stoeva, P. Balazs: Invertibility of multipliers, Appl. Comput. Harmon. Anal., 33 (2) (2012), 292–299.
  • D. T. Stoeva, P. Balazs: On the dual frame induced by an invertible frame multiplier, Sampl. Theory Signal and Image Proc., 15 (2016), 119–130.

Estimate of the spectral radii of Bessel multipliers and consequences

Yıl 2023, , 176 - 183, 15.09.2023
https://doi.org/10.33205/cma.1323956

Öz

Bessel multipliers are operators defined from two Bessel sequences of elements of a Hilbert space and a complex sequence, and have frame multipliers as particular cases. In this paper an estimate of the spectral radius of a Bessel multiplier is provided involving the cross Gram operator of the two sequences. As an upshot, it is possible to individuate some regions of the complex plane where the spectrum of a multiplier of dual frames is contained.

Destekleyen Kurum

European Union

Proje Numarası

FSE - REACT EU, PON Ricerca e Innovazione 2014-2020

Teşekkür

European Union, GNAMPA-INdAM

Kaynakça

  • R. Balan, P.G. Casazza, C. Heil and Z. Landau: Density, overcompleteness, and localization of frames I. Theory, J. Fourier Anal. Appl., 12 (2006), 105–143.
  • P. Balazs: Basic definition and properties of Bessel multipliers, J. Math. Anal. Appl., 325 (1) (2007), 571–585.
  • P. Balazs: Hilbert-Schmidt operators and frames-classification, best approximation by multipliers and algorithms, Int. J. Wavelets Multiresolut. Inf. Process., 6 (2) (2008), 315–330.
  • P. Balazs, B. Laback, G. Eckel and W.A. Deutsch: Time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking, IEEE Transactions on Audio, Speech, and Language Processing, 18 (1) (2010), 34–49.
  • P. Balazs, D. T. Stoeva: Representation of the inverse of a frame multiplier, J. Math. Anal. Appl., 422 (2) (2015), 981–994.
  • O. Christensen: An Introduction to Frames and Riesz Bases, second expanded edition, Birkhäuser, Boston, (2016).
  • J. Conway: A Course in Functional Analysis, Graduate Texts in Mathematics. 96 (2nd ed.), New York: Springer-Verlag, (1990).
  • E. Cordero, K. Gröchenig: Localization of frames II, Appl. Comput. Harmon. Anal., 17 (2004), 29–47.
  • R. Corso: On some dual frames multipliers with at most countable spectra, Ann. Mat. Pura Appl., 201 (4) (2022), 1705–1716.
  • R. Corso: Localization of the spectra of dual frames multipliers, Constr. Math. Anal., 5 (4) (2022), 238–245.
  • R. Corso, F. Tschinke: Some notes about distribution frame multipliers, in: Landscapes of Time-Frequency Analysis, vol. 2, P. Boggiatto, T. Bruno, E. Cordero, H.G. Feichtinger, F. Nicola, A. Oliaro, A. Tabacco, M. Vallarino (Ed.), Applied and Numerical Harmonic Analysis Series, Springer, (2020).
  • H. G. Feichtinger, K. Nowak: A first survey of Gabor multipliers, in: Advances in Gabor analysis, H. G. Feichtinger and T. Strohmer (Ed.), Boston Birkhäuser, Applied and Numerical Harmonic Analysis, (2003).
  • G. B. Folland: A Course in Abstract Harmonic Analysis, CRC Press, Boca, Raton, (1995).
  • J.-P. Gazeau: Coherent States in Quantum Physics, Weinheim: Wiley, (2009).
  • K. Gröchenig: Foundations of Time-Frequency Analysis, Birkhäauser, Boston, (2000).
  • K. Gröchenig: Localization of frames, Banach frames, and the invertibility of the frame operator, J. Fourier Anal. Appl., 10 (2004), 105–132.
  • K. Gröchenig, M. Fornasier: Intrinsic localization of frames, Constr. Approx., 22 (2005), 395–415.
  • E. Hernández, H. Šiki´c, G. Weiss and E. N. Wilson: Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform, Colloq. Math., 118 (1) (2010), 313–332.
  • H. Javanshiri, M. Abolghasemi, A.A. Arefijamaal: The essence of invertible frame multipliers in scalability, Adv. Comput. Math., 48 (2022), ARTICLE ID: 19.
  • T. Kato: Perturbation Theory for Linear Operators, Springer, Berlin, (1966).
  • G. Matz, F. Hlawatsch: Linear time-frequency filters: On-line algorithms and applications, in: A. Papandreou- Suppappola (Ed.), Application in Time-Frequency Signal Processing, CRC Press, Boca Raton, FL, (2002).
  • R. Levie, H. Avron: Randomized Signal Processing with Continuous Frames, J. Fourier Anal. Appl., 28 (2022), ARTICLE ID: 5.
  • K. Schmüdgen: Unbounded Self-adjoint Operators on Hilbert Space, Springer, Dordrecht, (2012).
  • D. T. Stoeva, P. Balazs: Invertibility of multipliers, Appl. Comput. Harmon. Anal., 33 (2) (2012), 292–299.
  • D. T. Stoeva, P. Balazs: On the dual frame induced by an invertible frame multiplier, Sampl. Theory Signal and Image Proc., 15 (2016), 119–130.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Lie Grupları, Harmonik ve Fourier Analizi, Operatör Cebirleri ve Fonksiyonel Analiz, Yaklaşım Teorisi ve Asimptotik Yöntemler
Bölüm Makaleler
Yazarlar

Rosario Corso 0000-0001-9123-4977

Proje Numarası FSE - REACT EU, PON Ricerca e Innovazione 2014-2020
Erken Görünüm Tarihi 8 Eylül 2023
Yayımlanma Tarihi 15 Eylül 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Corso, R. (2023). Estimate of the spectral radii of Bessel multipliers and consequences. Constructive Mathematical Analysis, 6(3), 176-183. https://doi.org/10.33205/cma.1323956
AMA Corso R. Estimate of the spectral radii of Bessel multipliers and consequences. CMA. Eylül 2023;6(3):176-183. doi:10.33205/cma.1323956
Chicago Corso, Rosario. “Estimate of the Spectral Radii of Bessel Multipliers and Consequences”. Constructive Mathematical Analysis 6, sy. 3 (Eylül 2023): 176-83. https://doi.org/10.33205/cma.1323956.
EndNote Corso R (01 Eylül 2023) Estimate of the spectral radii of Bessel multipliers and consequences. Constructive Mathematical Analysis 6 3 176–183.
IEEE R. Corso, “Estimate of the spectral radii of Bessel multipliers and consequences”, CMA, c. 6, sy. 3, ss. 176–183, 2023, doi: 10.33205/cma.1323956.
ISNAD Corso, Rosario. “Estimate of the Spectral Radii of Bessel Multipliers and Consequences”. Constructive Mathematical Analysis 6/3 (Eylül 2023), 176-183. https://doi.org/10.33205/cma.1323956.
JAMA Corso R. Estimate of the spectral radii of Bessel multipliers and consequences. CMA. 2023;6:176–183.
MLA Corso, Rosario. “Estimate of the Spectral Radii of Bessel Multipliers and Consequences”. Constructive Mathematical Analysis, c. 6, sy. 3, 2023, ss. 176-83, doi:10.33205/cma.1323956.
Vancouver Corso R. Estimate of the spectral radii of Bessel multipliers and consequences. CMA. 2023;6(3):176-83.