Araştırma Makalesi
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Localization of the spectra of dual frames multipliers

Yıl 2022, Cilt: 5 Sayı: 4, 238 - 245, 01.12.2022
https://doi.org/10.33205/cma.1154703

Öz

This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the paper is to give some results about the localization of the spectra of dual frames multipliers, i.e. to identify regions of the complex plane containing the spectra using some information about the frames and the symbols.

Kaynakça

  • F. Bagarello, A. Inoue and C. Trapani: Non-self-adjoint hamiltonians defined by Riesz bases, J. Math. Phys., 55 (2014), 033501.
  • P. Balazs: Basic definition and properties of Bessel multipliers, J. Math. Anal. Appl., 325 (1) (2007), 571–585.
  • P. Balazs, D. Bayer and A. Rahimi: Multipliers for continuous frames in Hilbert spaces, J. Phys. A: Math. Theor., 45 (24) (2012), 244023.
  • P. Balazs, N. Holighaus, T. Necciari and D. T. Stoeva: Frame theory for signal processing in psychoacoustics, excursions in harmonic analysis, In: Radu Balan, John J. Benedetto, Wojciech Czaja, and Kasso Okoudjou, eds., Applied and Numerical Harmonic Analysis, Vol. 5, Basel: Birkhäuser, 225–268, (2017).
  • 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).
  • R. Corso: Sesquilinear forms associated to sequences on Hilbert spaces, Monatsh. Math., 189 (4) (2019), 625-650.
  • R. Corso: On some dual frames multipliers with at most countable spectra, Ann. Mat. Pura Appl., 201 (4) (2022), 1705-1716.
  • 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).
  • I. Daubechies: Ten Lectures on Wavelets, SIAM, Philadelphia, (1992).
  • 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).
  • J.-P. Gazeau: Coherent States in Quantum Physics, Weinheim: Wiley (2009).
  • K. Gröchenig: Foundations of Time-Frequency Analysis, Birkhäauser, Boston (2000).
  • 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).
  • D. T. Stoeva, P. Balazs: Invertibility of multipliers, Appl. Comput. Harmon. Anal., 33 (2) (2012), 292-299.
  • D. T. Stoeva, P. Balazs: Detailed characterization of conditions for the unconditional convergence and invertibility of multipliers, Sampl. Theory Signal Image Process., 12 (2-3) (2013), 87-125.
  • D. T. Stoeva, P. Balazs: Riesz bases multipliers, In M. Cepedello Boiso, H. Hedenmalm, M. A. Kaashoek, A. Montes-Rodríguez, and S. Treil, editors, Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation, vol 236 of Operator Theory: Advances and Applications, 475-482. Birkhäuser, Springer Basel (2014).
  • D. T. Stoeva, P. Balazs: On the dual frame induced by an invertible frame multiplier, Sampling Theory in Signal and Image Processing, 15 (2016), 119-130.
  • D. T. Stoeva, P. Balazs: Commutative properties of invertible multipliers in relation to representation of their inverses, In Sampling Theory and Applications (SampTA), 2017 International Conference on, 288-293. IEEE, (2017).
  • D. T. Stoeva, P. Balazs: A survey on the unconditional convergence and the invertibility of multipliers with implementation, In: Sampling - Theory and Applications (A Centennial Celebration of Claude Shannon), S. D. Casey, K. Okoudjou, M. Robinson, B. Sadler (Ed.), Applied and Numerical Harmonic Analysis Series, Springer (2020).
  • C. Trapani, S. Triolo and F. Tschinke: Distribution Frames and Bases, J. Fourier Anal. and Appl., 25 (2019), 2109-2140.
Yıl 2022, Cilt: 5 Sayı: 4, 238 - 245, 01.12.2022
https://doi.org/10.33205/cma.1154703

Öz

Kaynakça

  • F. Bagarello, A. Inoue and C. Trapani: Non-self-adjoint hamiltonians defined by Riesz bases, J. Math. Phys., 55 (2014), 033501.
  • P. Balazs: Basic definition and properties of Bessel multipliers, J. Math. Anal. Appl., 325 (1) (2007), 571–585.
  • P. Balazs, D. Bayer and A. Rahimi: Multipliers for continuous frames in Hilbert spaces, J. Phys. A: Math. Theor., 45 (24) (2012), 244023.
  • P. Balazs, N. Holighaus, T. Necciari and D. T. Stoeva: Frame theory for signal processing in psychoacoustics, excursions in harmonic analysis, In: Radu Balan, John J. Benedetto, Wojciech Czaja, and Kasso Okoudjou, eds., Applied and Numerical Harmonic Analysis, Vol. 5, Basel: Birkhäuser, 225–268, (2017).
  • 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).
  • R. Corso: Sesquilinear forms associated to sequences on Hilbert spaces, Monatsh. Math., 189 (4) (2019), 625-650.
  • R. Corso: On some dual frames multipliers with at most countable spectra, Ann. Mat. Pura Appl., 201 (4) (2022), 1705-1716.
  • 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).
  • I. Daubechies: Ten Lectures on Wavelets, SIAM, Philadelphia, (1992).
  • 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).
  • J.-P. Gazeau: Coherent States in Quantum Physics, Weinheim: Wiley (2009).
  • K. Gröchenig: Foundations of Time-Frequency Analysis, Birkhäauser, Boston (2000).
  • 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).
  • D. T. Stoeva, P. Balazs: Invertibility of multipliers, Appl. Comput. Harmon. Anal., 33 (2) (2012), 292-299.
  • D. T. Stoeva, P. Balazs: Detailed characterization of conditions for the unconditional convergence and invertibility of multipliers, Sampl. Theory Signal Image Process., 12 (2-3) (2013), 87-125.
  • D. T. Stoeva, P. Balazs: Riesz bases multipliers, In M. Cepedello Boiso, H. Hedenmalm, M. A. Kaashoek, A. Montes-Rodríguez, and S. Treil, editors, Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation, vol 236 of Operator Theory: Advances and Applications, 475-482. Birkhäuser, Springer Basel (2014).
  • D. T. Stoeva, P. Balazs: On the dual frame induced by an invertible frame multiplier, Sampling Theory in Signal and Image Processing, 15 (2016), 119-130.
  • D. T. Stoeva, P. Balazs: Commutative properties of invertible multipliers in relation to representation of their inverses, In Sampling Theory and Applications (SampTA), 2017 International Conference on, 288-293. IEEE, (2017).
  • D. T. Stoeva, P. Balazs: A survey on the unconditional convergence and the invertibility of multipliers with implementation, In: Sampling - Theory and Applications (A Centennial Celebration of Claude Shannon), S. D. Casey, K. Okoudjou, M. Robinson, B. Sadler (Ed.), Applied and Numerical Harmonic Analysis Series, Springer (2020).
  • C. Trapani, S. Triolo and F. Tschinke: Distribution Frames and Bases, J. Fourier Anal. and Appl., 25 (2019), 2109-2140.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Rosario Corso 0000-0001-9123-4977

Yayımlanma Tarihi 1 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 4

Kaynak Göster

APA Corso, R. (2022). Localization of the spectra of dual frames multipliers. Constructive Mathematical Analysis, 5(4), 238-245. https://doi.org/10.33205/cma.1154703
AMA Corso R. Localization of the spectra of dual frames multipliers. CMA. Aralık 2022;5(4):238-245. doi:10.33205/cma.1154703
Chicago Corso, Rosario. “Localization of the Spectra of Dual Frames Multipliers”. Constructive Mathematical Analysis 5, sy. 4 (Aralık 2022): 238-45. https://doi.org/10.33205/cma.1154703.
EndNote Corso R (01 Aralık 2022) Localization of the spectra of dual frames multipliers. Constructive Mathematical Analysis 5 4 238–245.
IEEE R. Corso, “Localization of the spectra of dual frames multipliers”, CMA, c. 5, sy. 4, ss. 238–245, 2022, doi: 10.33205/cma.1154703.
ISNAD Corso, Rosario. “Localization of the Spectra of Dual Frames Multipliers”. Constructive Mathematical Analysis 5/4 (Aralık 2022), 238-245. https://doi.org/10.33205/cma.1154703.
JAMA Corso R. Localization of the spectra of dual frames multipliers. CMA. 2022;5:238–245.
MLA Corso, Rosario. “Localization of the Spectra of Dual Frames Multipliers”. Constructive Mathematical Analysis, c. 5, sy. 4, 2022, ss. 238-45, doi:10.33205/cma.1154703.
Vancouver Corso R. Localization of the spectra of dual frames multipliers. CMA. 2022;5(4):238-45.