M. A. Shubin, “Differential and pseudodifferential operators in spaces of almost periodic functions”, Math. USSR-Sb., 24:4 (1974), 547

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Mathematics of the USSR-Sbornik, 1974, Volume 24, Issue 4, Pages 547–573
DOI: https://doi.org/10.1070/SM1974v024n04ABEH001923 (Mi sm3769)

This article is cited in 18 scientific papers (total in 19 papers)

Differential and pseudodifferential operators in spaces of almost periodic functions

M. A. Shubin

English version PDF (1445 kB) Citations (19) Russian version article

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DOI: https://doi.org/10.1070/SM1974v024n04ABEH001923

Abstract: We construct a Sobolev-type space of almost periodic functions, in which we study differential and pseudodifferential operators. We show that the usual theorem on the regularity of solutions of elliptic equations is not true in these spaces, and we present modified variants of this theorem. We also study the question of the defect indices of differential operators in the space of Besicovitch almost periodic functions, and prove a Liouville-type theorem in this space.
Bibliography: 16 titles.

Received: 29.05.1974

Bibliographic databases:

UDC: 517.43

MSC: Primary 35J30, 35D05, 35S05, 47F05, 47G05, 42A84; Secondary 46E35

Language: English

Original paper language: Russian

Citation: M. A. Shubin, “Differential and pseudodifferential operators in spaces of almost periodic functions”, Math. USSR-Sb., 24:4 (1974), 547–573

Citation in format AMSBIB

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\by M.~A.~Shubin

\paper Differential and pseudodifferential operators in spaces of almost periodic functions

\jour Math. USSR-Sb.

\yr 1974

\vol 24

\issue 4

\pages 547--573

\mathnet{http://mi.mathnet.ru/eng/sm3769}

\crossref{https://doi.org/10.1070/SM1974v024n04ABEH001923}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=358445}

\zmath{https://zbmath.org/?q=an:0311.47022}

Linking options:

https://www.mathnet.ru/eng/sm3769

https://doi.org/10.1070/SM1974v024n04ABEH001923

https://www.mathnet.ru/eng/sm/v137/i4/p560

This publication is cited in the following 19 articles:

Fabio M Mele, Johannes Münch, “On the role of fiducial structures in minisuperspace reduction and quantum fluctuations in LQC”, Class. Quantum Grav., 41:24 (2024), 245003
Fabio M. Mele, Johannes Münch, “Physical relevance of the fiducial cell in loop quantum cosmology”, Phys. Rev. D, 108:10 (2023)
M. Braverman, V. M. Buchstaber, M. Gromov, V. Ivrii, Yu. A. Kordyukov, P. Kuchment, V. Maz'ya, S. P. Novikov, T. Sunada, L. Friedlander, A. G. Khovanskii, “Mikhail Aleksandrovich Shubin (obituary)”, Russian Math. Surveys, 75:6 (2020), 1143–1152
Norbert Bodendorfer, Fabio M Mele, Johannes Münch, “Is limiting curvature mimetic gravity an effective polymer quantum gravity?”, Class. Quantum Grav., 35:22 (2018), 225001
N. Bodendorfer, “Quantum reduction to Bianchi I models in loop quantum gravity”, Phys. Rev. D, 91:8 (2015)
Paolo Boggiatto, Carmen Fernández, Antonio Galbis, “Gabor systems and almost periodic functions”, Applied and Computational Harmonic Analysis, 2015
Desheng Ji, Chuanyi Zhang, “Pseudo almost periodic weak solutions of a semilinear elliptic equation”, Adv Diff Equ, 2014:1 (2014), 46
Alessandro Oliaro, Luigi Rodino, Patrik Wahlberg, “Almost periodic pseudodifferential operators and Gevrey classes”, Annali di Matematica, 2011
Patrik Wahlberg, “Representations of almost periodic pseudodifferential operators and applications in spectral theory”, J. Pseudo-Differ. Oper. Appl, 2011
Pierre-A. Vuillermot, “Almost-periodic attractors for a class of nonautonomous reaction-diffusion equations on N—III. Center curves and liapounov stability”, Nonlinear Analysis: Theory, Methods & Applications, 22:5 (1994), 533
Pierre-A Vuillermot, “Almost-periodic attractors for a class of nonautonomous reaction-diffusion equations on N. I. Global stabilization processes”, Journal of Differential Equations, 94:2 (1991), 228
Bruno Scarpellini, Pierre-A. Vuillermot, “Smooth manifolds for semilinear wave equations on 2: On the existence of almost-periodic breathers”, Journal of Differential Equations, 77:1 (1989), 123
P. E. Dedik, M. A. Shubin, “Random pseudodifferential operators and the stabilization of solutions of parabolic equations with random coefficients”, Math. USSR-Sb., 41:1 (1982), 33–52
M. A. Shubin, “The spectral theory and the index of elliptic operators with almost periodic coefficients”, Russian Math. Surveys, 34:2 (1979), 109–157
A. S. Mishchenko, “Banach algebras, pseudodifferential operators, and their application to $K$ -theory”, Russian Math. Surveys, 34:6 (1979), 77–91
V. I. Bezyaev, “Asymptotics of the density of states of hypoelliptic almost periodic operators”, Math. USSR-Sb., 34:4 (1978), 425–447
B. V. Fedosov, M. A. Shubin, “The index of random elliptic operators. II”, Math. USSR-Sb., 35:1 (1979), 131–156
M. A. Shubin, “Almost periodic functions and partial differential operators”, Russian Math. Surveys, 33:2 (1978), 1–52
M. A. Shubin, “Almost-periodic elliptic operators and von Neumann algebras”, Funct. Anal. Appl., 9:1 (1975), 88–89

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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