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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 175–192 (Mi mz4165)  

This article is cited in 23 scientific papers (total in 23 papers)

Linear Relations as Generators of Semigroups of Operators

A. G. Baskakov

Voronezh State University

Abstract: The theory of semigroups of bounded linear operators is based on the spectral theory of linear relations (multivalued linear operators), which act as generators of operator semigroups.

Keywords: semigroup, bounded linear operator, linear relation (multivalued linear operator), spectral theory, primitive generator of a semigroup, resolvent set of a linear relation, ergodic theorem, holomorphic function

DOI: https://doi.org/10.4213/mzm4165

Full text: PDF file (562 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2008, 84:2, 166–183

Bibliographic databases:

UDC: 517.984+517.986
Received: 22.03.2007
Revised: 15.01.2008

Citation: A. G. Baskakov, “Linear Relations as Generators of Semigroups of Operators”, Mat. Zametki, 84:2 (2008), 175–192; Math. Notes, 84:2 (2008), 166–183

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. S. Bichegkuev, “To the theory of infinitely differentiable semigroups of operators”, St. Petersburg Math. J., 22:2 (2011), 175–182  mathnet  crossref  mathscinet  zmath  isi
    2. Bichegkuev M.S., “On some classes of infinitely differentiable operator semigroups”, Differ. Equ., 46:2 (2010), 224–238  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. A. G. Chshiev, “The closeness and closability criteria for infinitesimal operators of certain semigroups”, Russian Math. (Iz. VUZ), 55:8 (2011), 66–74  mathnet  crossref  mathscinet  elib
    4. A. V. Pechkurov, “On the Structure of a Semigroup of Operators with Finite-Dimensional Ranges”, Math. Notes, 91:2 (2012), 231–242  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. Pastor J., “On uniqueness of fractional powers of multi-valued linear operators and the incomplete Cauchy problem”, Ann. Mat. Pura Appl. (4), 191:1 (2012), 167–180  crossref  mathscinet  zmath  isi  scopus
    6. A. G. Chshiev, “The Gearhart–Prüss Theorem for a Class of Degenerate Semigroups of Operators”, Math. Notes, 94:3 (2013), 400–413  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. A. G. Chshiev, “O polugruppe operatorov Silchenko”, Vladikavk. matem. zhurn., 15:4 (2013), 82–90  mathnet
    8. Baskakov A.G., Krishtal I.A., “On Completeness of Spectral Subspaces of Linear Relations and Ordered Pairs of Linear Operators”, J. Math. Anal. Appl., 407:1 (2013), 157–178  crossref  mathscinet  zmath  isi  elib  scopus
    9. Verdier O., “Reductions of Operator Pencils”, Math. Comput., 83:285 (2014), 189–214  crossref  mathscinet  zmath  isi  scopus
    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. V. M. Bruk, “On Linear Relations Generated by an Integro-Differential Equation with Nevanlinna Measure in the Infinite-Dimensional Case”, Math. Notes, 96:1 (2014), 10–25  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Alvarez T., Ammar A., Jeribi A., “On the Essential Spectra of Some Matrix of Linear Relations”, Math. Meth. Appl. Sci., 37:5 (2014), 620–644  crossref  mathscinet  zmath  isi  scopus
    13. A. G. Chshiev, “Ob obraschenii polugruppy operatorov”, Vladikavk. matem. zhurn., 16:2 (2014), 79–89  mathnet
    14. A. G. Baskakov, “Harmonic and Spectral Analysis of Power Bounded Operators and Bounded Semigroups of Operators on Banach Spaces”, Math. Notes, 97:2 (2015), 164–178  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. A. G. Baskakov, “Estimates for the Green's function and parameters of exponential dichotomy of a hyperbolic operator semigroup and linear relations”, Sb. Math., 206:8 (2015), 1049–1086  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. 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
    18. A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Math. Notes, 101:3 (2017), 391–405  mathnet  crossref  crossref  mathscinet  isi  elib
    19. Ammar A., Jeribi A., Saadaoui B., “Frobenius–Schur Factorization for Multivalued
      $${\varvec{2\times 2}}$$
      2 2 Matrices Linear Operator”, Mediterr. J. Math., 14:1 (2017), UNSP 29  crossref  mathscinet  isi  elib  scopus
    20. Baskakov A., Obukhovskii V., Zecca P., “Almost Periodic Solutions At Infinity of Differential Equations and Inclusions”, J. Math. Anal. Appl., 462:1 (2018), 747–763  crossref  mathscinet  zmath  isi  scopus
    21. Ammar A., “Some Results on Semi-Fredholm Perturbations of Multivalued Linear Operators”, Linear Multilinear Algebra, 66:7 (2018), 1311–1332  crossref  mathscinet  zmath  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, eds. Kim Y., Narayan S., Picioroaga G., Weber E., Amer Mathematical Soc, 2018, 93–114  crossref  mathscinet  isi  scopus
    23. M. S. Bichegkuev, “Almost periodic at infinity solutions to integro-differential equations with non-invertible operator at derivative”, Ufa Math. J., 12:1 (2020), 3–12  mathnet  crossref  isi
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