Related papers: Functional Equations and Fourier Analysis
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable…
The Donald--Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and for the classical Weyl groups (whose rational group…
In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions…
The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all…
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
This is the first of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
We compare and contrast three different methods for the construction of the differential relations satisfied by the fundamental Abelian functions associated with an algebraic curve. We realize these Abelian functions as logarithmic…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
There are ten chapters in this dissertation, which focuses on nine contents: growth estimates for a class of subharmonic functions in the half plane; growth estimates for a class of subharmonic functions in the half space; a generalization…
The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class…
Given a positive definite binary quadratic form f, let r(n) = |{(x,y): f(x,y)=n}| denote its representation function. In this paper we study linear correlations of these functions. For example, if r_1, ..., r_k are representation functions,…
We introduce a formal operational semantics that describes the fused execution of variable contraction problems, which compute indexed arithmetic over a semiring and generalize sparse and dense tensor algebra, relational algebra, and graph…
In this paper, we study the existence of solutions of the functional difference equations with proportional delay on deformed generalized Fibonacci polynomials via successive approximation method and Bell polynomials. First, we introduce…
We discuss the following topics: n-dimensional local fields and adelic groups; harmonic analysis on local fields and adelic groups for two-dimensional schemes (function spaces, Fourier transform, Poisson formula); representations of…
A series of problems in different fields such as physics and chemistry are modeled by differential equations. Differential equations are divided into partial differential equations and ordinary differential equations which can be linear or…
In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration. Under the condition (A), we get an integral representation formula for the…
Here we look at some situations that are like the unit circle or the real line in some ways, but which can be more complicated or fractal in other ways.