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.
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
This publication is cited in the following 28 articles:
Yanyan Du, Junjie Huang, “Essential spectra of upper triangular relation matrices”, Monatsh Math, 200:1 (2023), 43
Marko Kostic, “Abstract degenerate Volterra inclusions in locally convex spaces”, ejde, 2023:01-?? (2023), 63
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
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
Ammar A., “Some Results on Semi-Fredholm Perturbations of Multivalued Linear Operators”, Linear Multilinear Algebra, 66:7 (2018), 1311–1332
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
A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Math. Notes, 101:3 (2017), 391–405
Ammar A., Jeribi A., Saadaoui B., “Frobenius–Schur Factorization for Multivalued \varvec2×2 2 2 Matrices Linear Operator”, Mediterr. J. Math., 14:1 (2017), UNSP 29
Baskakov A.G. Krishtal I.A., “Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces”, Mediterr. J. Math., 13:5 (2016), 2443–2462
Aymen Ammar, Toka Diagana, Aref Jeribi, “Perturbations of Fredholm linear relations in Banach spaces with application to <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mn>3</mml:mn><mml:mo>×</mml:mo><mml:mn>3</mml:mn></mml:math>-”, Arab Journal of Mathematical Sciences, 22:1 (2016), 59
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
A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232
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
M. S. Bichegkuev, “Spectral analysis of differential operators with unbounded operator coefficients on the half-line”, Diff Equat, 51:4 (2015), 431
Aymen Ammar, Mohammed Zerai Dhahri, Aref Jeribi, “Some properties of upper triangular 3×3 3 × 3 -block matrices of linear relations”, Boll Unione Mat Ital, 8:3 (2015), 189
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
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
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
A. G. Chshiev, “Ob obraschenii polugruppy operatorov”, Vladikavk. matem. zhurn., 16:2 (2014), 79–89