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The main object of this paper is to study the generalized von mangoldt function using the L-additive function, which can help us give many result about the classical arithmetic function.
Construction of analytic functions, which determine bounded Toeplitz operators
Some notes and observations on analytic functions defined on an annulus
A Generalised Hadamard Transform for multi-phase or multilevel signals is introduced, which includes the Fourier, Generalised, Discrete Fourier, Walsh-Hadamard and Reverse Jacket Transforms. The jacket construction is formalised and shown…
In this paper, we establish three Landau-type theorems for certain bounded poly-analytic functions, which generalize the corresponding result for bi-analytic functions given by Liu and Ponnusamy [Canad. Math. Bull. 67(1): 2024, 152-165].…
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
\begin{abstract} We apply the theory of generalized Watson transforms developed in \cite{zheng00} to construct the complementary series of $GL(2,\R)$. \end{abstract}
In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as $\mathcal{L}_{\alpha,\mu}$-transform and generalized Stieltjes transform. In addition, we…
We give a systematic, abstract formulation of the image normalization method as applied to a general group of image transformations, and then illustrate the abstract analysis by applying it to the hierarchy of viewing transformations of a…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and…
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…
In this paper we introduce the concept of a convolution type operation of functionals on Wiener space. It contains several kinds of the concepts of convolution products on Wiener space, which have been studied by many authors. We then…
A general construction of transmutation operators is developed for selfadjoint operators in Gelfand triples. Theorems regarding analyticity of generalized eigenfunctions and Paley-Wiener properties are proved.
The general framework of Legendre transformation is extended to the case of symplectic groupoids, using an appropriate generalization of the notion of generating function (of a Lagrangian submanifold).
In this paper, we propose a numerical method of Fourier transform based on hyperfunction theory. In the proposed method, we compute analytic functions called the defining functions, which give the desired Fourier transform as a…