Related papers: Annihilation Operators for Exponential Spaces in S…
We consider the question when the so--called spectral condition} for Hermite subdivision schemes extends to spaces generated by polynomials and exponential functions. The main tool are convolution operators that annihilate the space in…
In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…
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…
For certain one-dimensional Schroedinger-type difference operators with a complex potential, a "complete" set of exponentially decaying eigenvectors is shown to exist. "Completeness" entails that the parameters involved are obtained through…
We discuss finite difference techniques for hyperbolic equations in non-trivial domains, as those that arise when simulating black hole spacetimes. In particular, we construct dissipative and difference operators that satisfy the {\it…
In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects. Our main result is the construction of an algebra of difference…
We construct parametrices for a class of pseudodifferential operators of infinite order acting on spaces of tempered ultradistributions of Beurling and Roumieu type. As a consequence we obtain a result of hypoellipticity in these spaces.
In this article, we study pseudo-differential equations involving semi-quasielliptic symbols over p-adics. We determine the function spaces where such equations have solutions. We introduce the space of infinitely pseudo-differentiable…
We propose two new definitions of the exponential function on time scales. The first definition is based on the Cayley transformation while the second one is a natural extension of exact discretizations. Our eponential functions map the…
Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.
We present an accurate investigation of the algebraic conditions that the symbols of a convergent, univariate, binary, non-stationary subdivision scheme should fulfill in order to reproduce spaces of exponential polynomials. A subdivision…
Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator…
The structure of exponential subspaces of finitely generated shift-invariant spaces is well understood and the role of such subspaces for the approximation power of refinable function vectors and related multi-wavelets is well studied. In…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…
We study the difference analog of the quotient differential operator from [Tarasov V., Uvarov F., Lett. Math. Phys. 110 (2020), 3375-3400, arXiv:1907.02117]. Starting with a space of quasi-exponentials $W=\langle \alpha_{i}^{x}p_{ij}(x),\,…
Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.
Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the…
We develop general expressions for the raising and lowering operators that belong to the orthogonal polynomials of hypergeometric type with discrete and continuous variable. We construct the creation and annihilation operators that…
It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions,…