Spectral Analysis of Differential Operators with Involution and Operator Groups

被引：0
作者：
A. G. Baskakov
N. B. Uskova
机构：
[1] Voronezh State University,
[2] Khetagurov North Ossetian State University,undefined
[3] Voronezh State Technical University,undefined
来源：
Differential Equations | 2018年 / 54卷
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摘要：
We study the spectral properties of differential operators with involution of the following two types: operators with involution multiplying the potential and operators with involution multiplying the derivative. The similar operator method is used to obtain a refined asymptotics of the eigenvalues and eigenvectors of such operators. These asymptotics are used to derive asymptotic formulas for the operator groups generated by the operators in question. These operator groups can be used to describe mild solutions of the corresponding mixed problems.
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页码：1261 / 1265
页数：4
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共 25 条
[1]  
Burlutskaya M.Sh.(2014)Mixed problem for simplest hyperbolic first order equations with involution Izv. Sarat. Univ. (N.S.), Ser. Mat. Mekh. Inform. 14 10-20
[2]  
Khromov A.P.(2014)Mixed problem for a first-order partial differential equation with involution and periodic boundary conditions Comput. Math. Math. Phys. 54 1-10
[3]  
Burlutskaya M.Sh.(2011)Initial-boundary value problems for first-order hyperbolic equations with involution Dokl. Math. 84 783-786
[4]  
Burlutskaya M.Sh.(2017)Riesz basis property of system of root functions of second-order differential operator with involution Differ. Equations 53 33-46
[5]  
Khromov A.P.(2017)Spectral analysis of a differential operator with an involution J. Evol. Equ. 17 669-684
[6]  
Kritskov L.V.(2018)A generalized Fourier method for the system of first-order differential equations with an involution and a group of operators Differ. Equations 54 277-281
[7]  
Sarsenbi A.M.(2018)Linear differential operator with an involution as a generator of an operator group Operators and Matrices 12 723-756
[8]  
Baskakov A.G.(2011)The method of similar operators in the spectral analysis of non-self-adjoint Dirac operators with nonsmooth potentials Izv. Math. 75 445-449
[9]  
Krishtal I.A.(2017)The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential Sb. Math. 208 1-43
[10]  
Romanova E.Yu.(2016)On the spectral properties of a second-order differential operator with a matrix potential Differ. Equations 52 557-567
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