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This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fr\'echet algebras, endowed with the topology of pointwise convergence. Our main results show…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
Functions like the exponential, Chebyshev polynomials, and monomial symmetric polynomials are preeminent among all special functions. They have simple definitions and can be expressed using easily specified integers like n!. Families of…
In the present paper, we investigate connections between various subclasses of harmonic univalent functions by using a convolution operator involving the Pascal distribution series.
Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to define convolution structures and modulus of smoothness for…
We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to…
We consider the Krall-Sheffer class of admissible, partial differential operators in the plane. We concentrate on algebraic structures, such as the role of commuting operators and symmetries. For the polynomial eigenfunctions, we give…
An implicit operation of a class of similar algebras $\mathsf{K}$ is a collection of first order definable partial functions on the members of $\mathsf{K}$ that is globally preserved by homomorphisms. For instance, "taking inverses" can be…
The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours through a motivating matrix completion problem. We give a…
We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of…
We give a number new examples analytically and numerically to confirm the Kohler conjecture. It turned out that for a rather large class of nonnegative functions the equality (A) hold.
We consider integrable open chain models formulated in terms of generators of affine Hecke algebras. The hierarchy of commutative elements (which are analogs of the commutative transfer-matrices) are constructed by using the fusion…
The convolution of a function with an isotropic Gaussian appears in many contexts such as differential equations, computer vision, signal processing, and numerical optimization. Although this convolution does not always have a closed form…
Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying…
The incomplete version of the Macdonald function has various appellations in literature and earns a well-deserved reputation of being a computational challenge. This paper ties together the previously disjoint literature and presents the…
The incomplete beta function is an important special function in statistics. In modern theory of hypergeometric functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles. However, the incomplete beta…
We present a generalization of standard Turing machines based on allowing unusual tapes. We present a set of reasonable constraints on tape geometry and classify all tapes conforming to these constraints. Surprisingly, this generalization…
We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.
We define an infinite series of translation coverings of Veech's double-n-gon for odd n greater or equal to 5 which share the same Veech group. Additionally we give an infinite series of translation coverings with constant Veech group of a…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…