Results 1 to 10 of about 27 (22)

Abstract Evolution Equations with an Operator Function in the Second Term

Axioms, 2022
In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations.
Maksim V. Kukushkin
doaj   +3 more sources

Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent

Mathematics, 2022
Our first aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten–von Neumann class of ...
Maksim V. Kukushkin
doaj   +3 more sources

Cauchy Problem for an Abstract Evolution Equation of Fractional Order

Fractal and Fractional, 2023
In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable.
Maksim V. Kukushkin
doaj   +3 more sources

Evolution Equations in Hilbert Spaces via the Lacunae Method

Fractal and Fractional, 2022
In this paper, we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation.
Maksim V. Kukushkin
doaj   +3 more sources

On the Essential Decreasing of the Summation Order in the Abel-Lidskii Sense

Mathematics
In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main
Maksim V. Kukushkin
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Note on the spectral theorem for unbounded non-selfadjoint operators

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022
In this paper, we deal with non-selfadjoint operators with the compact resolvent. Having been inspired by the Lidskii idea involving a notion of convergence of a series on the root vectors of the operator in a weaker – Abel-Lidskii sense, we proceed ...
Kukushkin, M.V.
doaj   +1 more source

Schatten Index of the Sectorial Operator via the Real Component of Its Inverse

Mathematics
In this paper, we study spectral properties of non-self-adjoint operators with the discrete spectrum. The main challenge is to represent a complete description of belonging to the Schatten class through the properties of the Hermitian real component. The
Maksim V. Kukushkin
doaj   +1 more source

Spectral Properties of the Nonsectorial Sturm–Liouville Operator on the Semiaxis

Mathematical Notes, 2023
Kh K Ishkin
exaly  

Derivatives of Symplectic Eigenvalues and a Lidskii Type Theorem

Canadian Journal of Mathematics, 2022
Tanvi Jain
exaly  

Lidskii's Theorem via Nonsmooth Analysis

SIAM Journal on Matrix Analysis and Applications, 2000
Adrian Lewis
exaly