1 citations · 2 across the 11 of their papers we have counts for
13 papers
On the essential decreasing of the summation order in the Abel-Lidskii sense
Maksim V. Kukushkin
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…
Kipriyanov's Fractional Calculus Prehistory and Legacy
Maksim V. Kukushkin
This paper is partly a historical survey of various approaches and methods in the fractional calculus, partly a description of the Kipriyanov extraordinary theory in comparison wit…
Schatten-von Neumann classes with more subtle asymptotics than one of the power type
Maksim V. Kukushkin
In this paper we study non-selfadjoint operators using the methods of the spectral theory. The main challenge is to represent a complete description of an operator belonging to the…
Cauchy Problem for an abstract Evolution Equation of fractional order
Maksim V. Kukushkin
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. In previous papers, we…
Abstract evolution equations with an operator function in the second term
Maksim V. Kukushkin
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. The main iss…
Evolution Equations in Hilbert Spaces via the Lacunae Method
Maksim V. Kukushkin
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. We establis…
Natural lacunae method and Schatten-von Neumann classes of the convergence exponent
Maksim V. Kukushkin
The first our 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 en…
One more theorem on norm equivalence in the Lebesgue space
Maksim V. Kukushkin
In this paper we consider a norm based on the infinitesimal generator of the shift semigroup in a direction. The relevance of such a focus is guaranteed by an abstract representati…
Convolution operators via orthogonal polynomials
Maksim Kukushkin
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achie…
On Smoothness of the Abel Equation Solution in Terms of the Jacoby Series Coefficients
Maksim V. Kukushkin
In this paper we continue the investigation of the Abel equation with the right part belonging to a Lebesgue weighted space. We have improved the previously known result - the uniq…
Abstract Fractional Calculus for m-accretive Operators
Maksim V. Kukushkin
In this paper we aim to construct an abstract model of a differential operator with a fractional integro-differential operator composition in final terms, where modeling is underst…
Riemann-Liouville Operator in Weighted L_p Spaces via the Jacobi Series Expansion
M. V. Kukushkin
In this paper we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann-Liouville fractional integral and derivative operators on a compact of the real…
Asymptotics of Eigenvalues for Differential Operators of Fractional Order
M. V. Kukushkin
In this paper we deal with a second order multidimensional fractional differential operator. We consider a case where the leading term represented by the uniformly elliptic operato…