26 citations · 75 across the 43 of their papers we have counts for
17 papers · 1 filter
On the connections of Hille-Phillips functional calculus with Bochner-Phillips functional calculus
A. R. Mirotin
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is considered. Connections of this calculus to Bochner-Phillips funct…
The unbounded extension of Hille-Phillips functional calculus
A. R. Mirotin
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is given. Connections of this calculus to Bochner-Phillips functional…
On sums and products of periodic functions
A. R. Mirotin, E. A. Mirotin
The main purpose of this work is to ascertain when arithmetic operations with periodic functions whose domains may not coincide with the whole real line preserve periodicity.
Equations of the first kind and the inversion of series of resolvents of a closed operator
A. R. Mirotin
Let be a densely defined closed operator in a complex Banach space Conditions for left invertibility of operators of the form are giv…
Analog for the Wiener Lemma for Wolff-Denjoy Series
A. R. Mirotin, A. A. Atvinovskii
Let a function f with real poles be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the note states that if we subtract its linear part from the fu…
On properties of Bernstein functions of several complex variables
A. R. Mirotin
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integr…
On Shilov boundary and Gelfand spectrum of algebras of generalized analytic functions
A. R. Mirotin
Let be a discrete abelian semigroup with unit and concellations and the semigroup of semicharacters of . We shaw that the strong boundary and the Shilov bound…
Fredholm and spectral properties of Toeplitz operators on spaces over ordered groups
A. R. Mirotin
Toeplitz operators on spaces associated with compact connected Abelian group with ordered dual are considered and the generalization of the classical Go…
Some assertions that are equivalent to Riemann hypothesis
A. R. Mirotin
Some assertions in harmonic analysis on the infinite dimensional torus are stated and their equivalence to Riemann hypothesis is proved.
On multidimensional Bochner-Phillips functional calculus
A. R. Mirotin
The functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the condition for holomorphy of semigroups, generated…
On the essential spectrum of -Toeplitz operators over compact Abelian groups
A. R. Mirotin
In the recent paper by Mark C. Ho (2014) the notion of a -Toeplitz operator on the Hardy space over the one-dimensional torus was introduced and i…
Functions of bounded mean oscillation and Hankel operators on compact abelian groups
A. R. Mirotin, R. V. Dyba
Generalization of functions of bounded mean oscillation and Hankel operators to the case of compact abelian groups with linearly ordered dual is considered. Spaces of functions of…
On some properties of multidimensional Bochner-Phillips functional calculus
A. R. Mirotin
The multidimensional functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the spectral mapping theorems for joi…
On joint spectra of families of unbounded operators
A. R. Mirotin
In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier…
The Paley-Wiener-Gelfand tauberian theorem for semigroups with invariant measure
A. R. Mirotin
The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several co…
Criteria for analyticity of subordinate semigroups
A. R. Mirotin
Let be a Bernstein function. A.~Carasso and T.~Kato obtained necessary and sufficient conditions for to have a property that generates a quasibounded holomorphic sem…
On the description of multidimensional normal Hausdorff operators on Lebesgue spaces
A. R. Mirotin
The main goal of this work is to examine the structure of normal Hausdorff operators on . We show that normal Hausdorff operator in is unitary equ…