26 citations · 75 across the 43 of their papers we have counts for
44 papers
On the regularity of generic Hausdorff-type transformations
A. R. Mirotin
The general notion of a Hausdorff-type operator with a kernel depending on an external variable is introduced and generalizations and analogs of classical results on the regularity…
Boundedness of Hausdorff-type operators with two-variable kernels on Lebesgue spaces
A. R. Mirotin
A general concept of a Hausdorff-type operator that absorbs all types of operators bearing the name `` Hausdorff operator'' and many others is considered. The characteristic featur…
On boundedness of Hausdorff-type operators on Sobolev spaces
A. R. Mirotin
A new notion of a Hausdorff-type operator on function spaces over domains in Euclidean spaces is introduced, and a sufficient condition for the boundedness of this operator on Sobo…
On a general concept of a Hausdorff-type operator
A. R. Mirotin
A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are give…
On the symbol calculus for multidimensional Hausdorff operators
E. Liflyand, A. Mirotin
The aim of this work is to derive a symbol calculus on for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent p…
On the spectra of multidimensional normal discrete Hausdorff operators
A. R. Mirotin
In the paper the general case of a normal discrete Hausdorff operators in is considered. The main result states that under some natural arithmetic condition the…
Some remarks on the solution of the cell growth equation
Adolf Mirotin
The analytical solution to the initial-boundary value problem for the cell growth equation was given in the paper Zaidi A. A., Van Brunt B., Wake G.C., Solutions to an advanced fun…
Algebras of Hausdorff Operators on the Real Line
E. Liflyand, A. Mirotin
The aim of this work is to derive a symbol calculus on for one-dimensional Hausdorff operators in apparently the most general form.
Hausdorff Operators on Compact Abelian Groups
A. R. Mirotin
Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces , real Hardy space , , and $…
Hausdorff Operators on Some Spaces of Holomorphic Functions on the Unit Disc
A. R. Mirotin
We introduce Hausdorff operators over the unit disc and give conditions for boundedness of such operator in Bloch, Bergman, and Hardy spaces on the disc. Identity approximation by…
A Hausdorff Operator on Lebesgue Space With Commuting Perturbation Matrices Is a Non-Riesz Operator
A. R. Mirotin
We consider a generalization of Hausdorff operators on Lebesgue spaces and under natural conditions prove that such an operator is not a Riesz operator provided it is non-zero. In…
On the boundedness of Hausdorff operators on real Hardy spaces over homogeneous spaces of groups with local doubling property
A. R. Mirotin
We give conditions for boundedness of Hausdorff operators on real Hardy spaces over homogeneous spaces of locally compact groups with local doubling property. The special cas…
On compact Hankel operators over compact Abelian groups
A. R. Mirotin
We consider compact and connected Abelian group with a linearly ordered dual. Based on the description of the structure of compact Hankel operators over , generalizations of…
On Hausdorff operators on homogeneous spaces of locally compact groups
A. R. Mirotin
Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators…
Hausdorff operators on Lebesgue spaces with positive definite perturbation matrices are non-Riesz
A. R. Mirotin
We consider generalized Hausdorff operators with positive definite and permutable perturbation matrices on Lebesgue spaces and prove that such operators are not Riesz operators pro…
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.