Duhamel Algebras and Applications

Karaev, M. T.

doi:10.1007/s10688-018-0201-z

Cited by 8 publications

(3 citation statements)

References 9 publications

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“…for some polynomials w p independent of x ∈ H(Q). Therefore, according to (29), for any z ∈ C we have…”

Section: (Iii)⇒(i)mentioning

confidence: 99%

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Coefficients of Exponential Series for Analytic Functions and the Pommiez Operator

Мелихов

2021

J Math Sci

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In this paper, we present results of the existence of a linear continuous right inverse operator for the operator of the representation of analytic functions in a bounded convex domain of the complex plane by series of quasi-polynomials and exponentials. We also present closely related results on the A. F. Leontiev interpolating function and, more generally, on the interpolating functional and the corresponding Pommiez operator. We examine cyclic vectors and closed invariant subspaces of the Pommiez operator in weighted spaces of entire functions.

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“…for some polynomials w p independent of x ∈ H(Q). Therefore, according to (29), for any z ∈ C we have…”

Section: (Iii)⇒(i)mentioning

confidence: 99%

“…The interest in it is due not the least to its obvious connection with the classical Volterra operator. For results related to the Duhamel multiplication and its various applications, see the works of M. T. Karaev [28,29].…”

Section: (Iii)⇒(i)mentioning

confidence: 99%

Coefficients of Exponential Series for Analytic Functions and the Pommiez Operator

Мелихов

2021

J Math Sci

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“…It is being studied quite intensively (see the paper of M.T. Karaev [8]). This multiplication is used in the theory of ordinary differential equations with constant coefficients, in the boundary value problem of mathematical physics (in the sloping beach problem), in the spectral theory of direct sums of operators.…”

Section: Introductionmentioning

confidence: 99%

On commutant of differentiation and translation operators in weighted spaces of entire functions

Иванова¹,

Мелихов²,

Melikhov³

2017

Ufimskii Matematicheskii Zhurnal

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Abstract. We describe continuous linear operators acting in a countable inductive limit of weighted Fréchet spaces of entire functions of several complex variables and commuting in these spaces with systems of partial differentiation and translation operators. Under the made assumptions, the commutants of the systems of differentiation and translation operators coincide. They consist of convolution operators defined by an arbitrary continuous linear functional on . At that, we do not assume that the set of the polynomials is dense in . In the space ′ topological dual to , we introduce the natural multiplication. Under this multiplication, the algebra ′ is isomorphic to the aforementioned commutant with the usual multiplication, which is the composition of the operators. This isomorphism is also topological if ′ is equipped by the weak topology, while the commutant is equipped by the weak operator topology. This implies that the set of the polynomials of the differentiation operators is dense in the commutant with topology of pointwise convergence. We also study the possibility of representing an operator in the commutant as an infinite order differential operator with constant coefficients. We prove the immediate continuity of linear operators commuting with all differentiation operators in a weighted (LF)-space of entire functions isomorphic via Fourier-Laplace transform to the space of infinitely differentiable functions compactly supported in a real multi-dimensional space.

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On the Commutant of the Generalized Backward Shift Operator in Weighted Spaces of Entire Functions

Иванова

Мелихов

2021

Trends in Mathematics

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Duhamel Algebras and Applications

Cited by 8 publications

References 9 publications

Coefficients of Exponential Series for Analytic Functions and the Pommiez Operator

Coefficients of Exponential Series for Analytic Functions and the Pommiez Operator

On commutant of differentiation and translation operators in weighted spaces of entire functions

On the Commutant of the Generalized Backward Shift Operator in Weighted Spaces of Entire Functions

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