Related papers: Elements of harmonic analysis, 3
This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…
We extend the notions of quantum harmonic analysis, as introduced in R. Werner's paper from 1984 (J. Math. Phys. 25(5)), to abelian phase spaces, by which we mean a locally compact abelian group endowed with a Heisenberg multiplier. In this…
We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the…
Making use of nonabelian harmonic analysis and representation theory, we solve the functional equation $$f_1(xy)+f_2(yx)+f_3(xy^{-1})+f_4(y^{-1}x)=f_5(x)f_6(y)$$ on arbitrary compact groups. The structure of its general solution is…
We study Stepanov and Weyl almost periodic functions on locally compact Abelian groups, which naturally appear in the theory of aperiodic order.
This paper concentrates on positive definite functions on finite abelian groups, which are central to harmonic analysis and related fields. By leveraging the group structure and employing Fourier analysis, we establish a lower bound for the…
We discuss various forms of the Plancherel Formula and the Plancherel Theorem on reductive groups over local fields.
This work addresses an extension of Fourier-Stieltjes transform of a vector measure defined on compact groups to locally compact groups, by using a group representation induced by a representation of one of its compact subgroups.
This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…
We continue in this paper the study of locally minimal groups started in \cite{LocMin}. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian…
We prove a Freiman-type theorem for locally compact abelian groups. If A is a subset of a locally compact abelian group with Haar measure m and m(nA) < n^dm(A) for all n>d log d then we describe A in a way which is tight up to logarithmic…
The paper discuss the limit point concept of a subset in a group via ideal of the power set ring. This idea along with anti-ideal give the topological structure in a group. Homomorphic images of both ideal and anti-ideal are played the…
We present characterizations of democratic property for systems of translates on a general locally compact abelian group, along a lattice in that group. That way we generalize the results from [11] on systems of integer translates.…
In this article, we study spectral Barron spaces whose elements are made up of some vector-valued functions on a compact group whose Fourier transforms admit a certain summability property. We investigate their functional properties and…
These notes briefly consider convolutions of tempered distributions with functions in the Schwartz class.
In this note some properties of the sum of element orders of a finite abelian group are studied.
We survey old and new results about the cohomology of the moduli space $A_g$ of principally polarized abelian varieties of genus $g$ and its compactifications. The main emphasis lies on the computation of the cohomology for small genus and…
We introduce a new notion of Almgren's frequency which is adapted to solutions of a sub-Laplacian (harmonic functions) on a Carnot group of arbitrary step $\bG$. With this notion we investigate some new functionals associated with the…