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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 3, Pages 3–54 (Mi izv639)  

This article is cited in 26 scientific papers (total in 26 papers)

Harmonic analysis of causal operators and their spectral properties

A. G. Baskakov, I. A. Krishtal


Abstract: The definition and study of causal operators are based on the representation theory of group algebras. We study the structure of the spectra of causal operators, obtain conditions for causal invertibility and state criteria for a causal operator to belong to the radical.

DOI: https://doi.org/10.4213/im639

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English version:
Izvestiya: Mathematics, 2005, 69:3, 439–486

Bibliographic databases:

UDC: 517.984.3
MSC: 47E05, 46H25, 47A35, 47D03, 47A06, 34G10, 47A10
Received: 22.01.2004

Citation: A. G. Baskakov, I. A. Krishtal, “Harmonic analysis of causal operators and their spectral properties”, Izv. RAN. Ser. Mat., 69:3 (2005), 3–54; Izv. Math., 69:3 (2005), 439–486

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Aldroubi A., Baskakov A., Krishtal I., “Slanted matrices, Banach frames, and sampling”, J. Funct. Anal., 255:7 (2008), 1667–1691  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. G. Baskakov, “Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations”, Izv. Math., 73:2 (2009), 215–278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. A. G. Baskakov, K. A. Sintyaeva, “On the Bohr–Favard inequalities for operators”, Russian Math. (Iz. VUZ), 53:12 (2009), 11–17  mathnet  crossref  mathscinet  zmath  elib
    4. Balan R., Krishtal I., “An almost periodic noncommutative Wiener's Lemma”, J. Math. Anal. Appl., 370:2 (2010), 339–349  crossref  mathscinet  zmath  isi  elib  scopus
    5. Krishtal I.A., “Wiener's Lemma and Memory Localization”, J. Fourier Anal. Appl., 2011  crossref  mathscinet  isi  elib  scopus
    6. A. G. Baskakov, N. S. Kaluzhina, “Beurlings theorem for functions with essential spectrum from homogeneous spaces and stabilization of solutions of parabolic equations”, Math. Notes, 92:5 (2012), 587–605  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. M. S. Bichegkuev, “Spectral analysis of difference and differential operators in weighted spaces”, Sb. Math., 204:11 (2013), 1549–1564  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. E. E. Dikarev, “On Bernstein inequality for vectors in Banach spaces”, Ufa Math. J., 5:4 (2013), 75–81  mathnet  crossref  elib
    9. I. I. Strukova, “O garmonicheskom analize periodicheskikh na beskonechnosti funktsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:1 (2014), 28–38  mathnet
    10. A. G. Baskakov, N. S. Kaluzhina, D. M. Polyakov, “Slowly varying on infinity semigroups of operators”, Russian Math. (Iz. VUZ), 58:7 (2014), 1–10  mathnet  crossref
    11. I. I. Strukova, “Harmonic Analysis of Periodic Vectors and Periodic at Infinity Functions”, J. Math. Sci., 211:6 (2015), 874–885  mathnet  crossref
    12. Baskakov A.G. Krishtal I.A., “Memory Estimation of Inverse Operators”, J. Funct. Anal., 267:8 (2014), 2551–2605  crossref  mathscinet  zmath  isi  scopus
    13. A. A. Ryzhkova, I. A. Trishina, “O pochti periodicheskikh na beskonechnosti resheniyakh raznostnykh uravnenii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:1 (2015), 45–49  mathnet  crossref  elib
    14. Ilya Krishtal, Thomas Strohmer, Tim Wertz, “Localization of Matrix Factorizations”, Found Comput Math, 15:4 (2015), 931  crossref  mathscinet  zmath  scopus
    15. I. I. Strukova, “On Wiener's Theorem for functions periodic at infinity”, Siberian Math. J., 57:1 (2016), 145–154  mathnet  crossref  crossref  mathscinet  isi  elib
    16. Baskakov A.G., Krishtal I.A., “Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces”, Mediterr. J. Math., 13:5 (2016), 2443–2462  crossref  mathscinet  zmath  isi  scopus
    17. A. Baskakov, I. Strukova, “Harmonic analysis of functions periodic at infinity”, Eurasian Math. J., 7:4 (2016), 9–29  mathnet
    18. I. I. Strukova, “Garmonicheskii analiz periodicheskikh na beskonechnosti funktsii v prostranstvakh Stepanova”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:2 (2017), 172–182  mathnet  crossref  elib
    19. I. I. Strukova, “Garmonicheskii analiz periodicheskikh na beskonechnosti funktsii v odnorodnykh prostranstvakh”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 2(39), 29–38  mathnet  crossref
    20. I. A. Trishina, “Pochti periodicheskie na beskonechnosti funktsii otnositelno podprostranstva integralno ubyvayuschikh na beskonechnosti funktsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:4 (2017), 402–418  mathnet  crossref  elib
    21. Baskakov A.G. Krishtal I.A., “Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces, II”, Mediterr. J. Math., 14:4 (2017), UNSP 181  crossref  mathscinet  isi  scopus
    22. Baskakov A.G. Krishtal I.A., “Spectral Properties of An Operator Polynomial With Coefficients in a Banach Algebra”, Frames and Harmonic Analysis, Contemporary Mathematics, 706, ed. Kim Y. Narayan S. Picioroaga G. Weber E., Amer Mathematical Soc, 2018, 93–114  crossref  mathscinet  isi  scopus
    23. Kurbatov V.G., Kuznetsova V.I., “On Stability of Linear Periodic Differential Difference Equations”, Quaest. Math., 41:4 (2018), 565–584  crossref  mathscinet  zmath  isi  scopus
    24. A. G. Baskakov, V. E. Strukov, I. I. Strukova, “On the almost periodic at infinity functions from homogeneous spaces”, Probl. anal. Issues Anal., 7(25):2 (2018), 3–19  mathnet  crossref  elib
    25. A. G. Baskakov, E. E. Dikarev, “Spectral theory of functions in studying partial differential operators”, Ufa Math. J., 11:1 (2019), 3–18  mathnet  crossref  isi
    26. Baskakov A.G. Krishtal I.A. Uskova N.B., “Similarity Techniques in the Spectral Analysis of Perturbed Operator Matrices”, J. Math. Anal. Appl., 477:2 (2019), 930–960  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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