Related papers: Reconstruction of functions from their triple corr…
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…
The graph reconstruction conjecture asserts that every simple graph on at least three vertices is uniquely determined by its deck of vertex-deleted subgraphs. In this expository article we survey the conjecture and present an…
We define a function by refining Stern's diatomic sequence. We name it the {\it assembly function}. It is strictly increasing continuous. The first and the second main theorems are on an action to the function. The third theorem is on…
A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of…
New class of special functions of three real variables, based on the alternating subgroup of the permutation group $S_3$, is studied. These functions are used for Fourier-like expansion of digital data given on lattice of any density and…
Three dimensional continuous and discrete Fourier-like transforms, based on the three simple and four semisimple compact Lie groups of rank 3, are presented. For each simple Lie group, there are three families of special functions ($C$-,…
We study sets $V$ in the tridisc that are relatively polynomially convex and have the polynomial extension property. If $V$ is one-dimensional, and is either algebraic, or has polynomially convex projections, we show that it is a retract.…
We study very smooth functions on the real line, namely Schwartz functions, that satisfy a finite identity relating their translates and a single modulation. Concretely, we assume there is a nontrivial linear combination of translates of…
The Replica Fourier Transform introduced previously is related to the standard definition of Fourier transforms over a group. Its use is illustrated by block-diagonalizing the eigenvalue equation of a four-replica Parisi matrix.
We propose the categorification of the algebraic analysis as the Leibniz 3-category given by generators and relations, including the Leibniz 3-cell relation. The Leibniz category offers the `most general' `(co-)derivation' 3-cell. We…
We study the third moment for functions on arbitrary compact Lie groups. We use techniques of representation theory to generalize the notion of band-limited functions in classical Fourier theory to functions on the compact groups $SU(n),…
We explore the analytic structure of three-point functions using contour deformations. This method allows continuing calculations analytically from the spacelike to the timelike regime. We first elucidate the case of two-point functions…
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
In general the endomorphisms of a non-abelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group which are endomorphisms when…
We say that a function $f \in L^1(\mathbb{R})$ tiles at level $w$ by a discrete translation set $\Lambda \subset \mathbb{R}$, if we have $\sum_{\lambda \in \Lambda} f(x-\lambda)=w$ a.e. In this paper we survey the main results, and prove…
In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also…
We describe an algorithm to decompose rational functions from which we determine the poset of groups fixing these functions.
We elaborate on the consequences of the factorization of the transfer matrix of any lossless multilayer in terms of three basic matrices of simple interpretation. By considering the bilinear transformation that this transfer matrix induces…
This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations. The classification recovers the classical transformations…