Related papers: Notes on normed algebras, 3

In these notes we focus on commutative finite-dimensional normed algebras and some basic examples.

These notes briefly discuss finite-dimensional algebras with involutions, self-adjoint elements, and so on.

These notes deal with algebras equipped with an involution and related matters.

Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the…

These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.

In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…

This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings.

In this short note, we treat an unbalanced shifted convolution sum of Fourier coefficients of cusp forms by a rather simple argument. Our result improves previous results established by more advanced approaches.

There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work arXiv:1803.01830, such partial sums are related to the radial asymptotics of infinite…

In this note, we study the arithmetic nature of values of modular functions, meromorphic modular forms and meromorphic quasi-modular forms with respect to arbitrary congruence subgroups, that have algebraic Fourier coefficients. This…

Fourier series with absolutely summable coefficients provide a classical example of a commutative Banach algebra, and these notes are concerned with this and related matters.

This paper continues the study of Fourier transforms on finite inverse semigroups, with a focus on Fourier inversion theorems and FFTs for new classes of inverse semigroups. We begin by introducing four inverse semigroup generalizations of…

These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.

These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.

We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.

A transitive permutation group is said to be semiprimitive if each of its normal subgroups is either semiregular or transitive.The class of semiprimitive groups properly contains primitive groups, quasiprimitive groups and innately…

We extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its…

We formulate a relationship between finite-order rondle invariants with respect to triple-point modifications and the lower central series of subgroups of a pure twin group. Using our formulation, we construct infinitely many infinite…

We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results…

In this paper we study algebraic supergroups and their coadjoint orbits as affine algebraic supervarieties. We find an algebraic deformation quantization of them that can be related to the fuzzy spaces of non commutative geometry.