相关论文: Rational hyperholomorphic functions in (\mathbb R^…
As was the case in a previous paper, the differential form x+ydxdy plays the role that the variable z plays in the standard calculus of complex variable. The role of holomorphic functions will now be played by strict harmonic differential…
We introduce the notion of Dunkl positive definite and strictly positive definite functions on $\mathbb{R}^{d}$. This done by the use of the properties of Dunkl translation. We establish the analogue of Bochner's theorem in Dunkl setting.…
We study reproducing kernel Hilbert and Pontryagin spaces of slice hyperholomorphic functions which are analogs of the Hilbert spaces of analytic functions introduced by de Branges and Rovnyak. In the first part of the paper we focus on the…
Partition functions of certain classes of "spin glass" models in statistical physics show strong connections to combinatorial graph invariants. Also known as homomorphism functions they allow for the representation of many such invariants,…
This paper introduces a new generalized superfactorial function (referable to as $n^{th}$- degree superfactorial: $sf^{(n)}(x)$) and a generalized hyperfactorial function (referable to as $n^{th}$- degree hyperfactorial: $H^{(n)}(x)$), and…
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…
Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and…
We prove a Cauchy-type integral representation for classes of functions holomorphic in four priviledged tuboid domains of the complexified one-sheeted two-dimensional hyperboloid. From a physical viewpoint, this hyperboloid can be used for…
We present two algorithms for constructing orthonormal bases of rational function vectors with respect to a discrete inner product, and discuss how to use them for a rational approximation problem. Building on the pencil-based formulation…
We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight…
We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commutation relations between double-row operators, we prove a skew…
In this paper we introduce and study some basic properties of the Fock space (also known as Segal-Bargmann space) in the slice hyperholomorphic setting. We discuss both the case of slice regular functions over quaternions and also the case…
In this article, the authors survey and review the studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. Its theoretical bases consist of the generalized…
We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
We prove that the Nevalinna-Pick algorithm provides different homeomorphisms between certain topological spaces of measures, analytic functions and sequences of complex numbers. This algorithm also yields a continued fraction expansion of…
Solovay proved that there exists a computable upper bound f of the prefix-free Kolmogorov complexity function K such that f (x) = K(x) for infinitely many x. In this paper, we consider the class of computable functions f such that K(x) <= f…
In this paper we characterise univariate rational functions over a number field $\K$ having infinitely many points in the cyclotomic closure $\K^c$ for which the orbit contains a root of unity. Our results are similar to previous results of…
The properties of the Wilson rational functions ${}_{10}\phi_9$ with three different normalizations are described. For one normalization, it satisfies an $R_{II}$ recurrence relation, whereas for the two other ones, they satisfy a…