相关论文: Infinite Order Differential Operators in Spaces of…
A scale of the Frechet spaces of exponential type entire functions of one complex variable is considered. Certain special properties of subsets of these spaces consisting of Laguerre entire functions, which are obtained as uniform limits on…
Infinite order differential operators appear in different fields of mathematics and physics. In the past decade they turned out to play a crucial role in the theory of superoscillations and provided new insight in the study of the evolution…
Infinite order differential operators appear in different fields of Mathematics and Physics and in the last decades they turned out to be of fundamental importance in the study of the evolution of superoscillations as initial datum for…
We study the effect of finite difference operators of finite order on the distribution of zeros of polynomials and entire functions.
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
The aim of this paper is to characterize continuous endomorphisms in the space of entire functions of exponential type of order $p>0$. Let $A_p$ denote the space of entire functions of $n$ complex variables $z\in{\mathbb C}^n$ of order $p$…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
In the first part of this work, we study the absolutely continuous operators which are defined on fuction spaces with wide sense. In the second part, we show some results concerning the absoltely continuous operators when the function…
We study the copolynomials of $n$ variables, i.e. $K$-linear mappings from the ring of polynomials $K[x_1,...,x_n]$ into the commutative ring $K$. We prove an existence and uniqueness theorem for a linear differential equation of infinite…
We develop a theory of pseudodifferential operators of infinite order for the global classes $\mathcal{S}_{\omega}$ of ultradifferentiable functions in the sense of Bj\"orck, following the previous ideas given by Prangoski for…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…
Specific global symbol classes and corresponding pseudodifferential operators of infinite order that act continuously on the space of tempered ultradistributions of Beurling and Roumieu type are constructed. For these classes, symbolic…
We completely describe all finite difference operators of the form $$ \Delta_{M_1, M_2, h}(f)(z)=M_1(z) f(z+h) + M_2(z) f(z-h) $$ preserving the Laguerre-P\'olya class of entire functions. Here $M_1$ and $M_2$ are some complex functions and…
We prove maximal regularity results in H\"older and Zygmund spaces for linear stationary and evolution equations driven by a large class of differential and pseudo-differential operators L, both in finite and in infinite dimension. The…
We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
We study the well-posedness of a Cauchy problem associated with the general form of the Laguerre operator and relate it to the corresponding global problem for the harmonic oscillator. To this end, we carry out a detailed analysis of the…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
We present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the…