相关论文: Notes on commutative algebra and harmonic analysis

The Fourier series of continuous functions of constant absolute value have interesting properties : according to the main theorems of the article, if the coefficients with positive indexes are square-summable with respect to a certain…

Polyadic arithmetics is a branch of mathematics related to $p$--adic theory. The aim of the present paper is to show that there are very close relations between polyadic arithmetics and the classic theory of commutative Banach algebras.…

We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…

We establish two general theorems on the local properties of the absolute summability of factored Fourier series by applying a recently defined absolute summability, $\left\vert A,\alpha_{n}\right\vert _{k}$ summability, and the class…

Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…

Let $E$ be a Banach space that does not contain any copy of $\ell^1$ and $\A$ be a non commutative $C^*$-algebra. We prove that every absolutely summing operator from $\A$ into $E^*$ is compact, thus answering a question of Pe\l czynski. As…

We show that each maximal ideal in a commutative Banach algebra has codimension 1.

The degenerate exponentials play an important role in recent study on degenerate versions of many special numbers and polynomials, the degenerate gamma function, the degenerate umbral calculus and the degenerate q-umbral calculus. The aim…

Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are…

We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…

We prove that the space of cuspidal quaternionic modular forms on the groups of type $F_4$ and $E_n$ have a purely algebraic characterization. This characterization involves Fourier coefficients and Fourier-Jacobi expansions of the cuspidal…

Let $E_{1},...,E_{m},F$ be Banach spaces. The index of summability of $\left(E_{1}\times\cdots\times E_{m},F\right) $ is a kind of measure of how far the $m$-linear operators $T:E_{1}\times\cdots\times E_{m}\rightarrow F$ are from being…

In this note we use recent results concerning the sum theorem for maximal monotone multifunctions in general Banach spaces to find new characterizations and properties of regular maximal monotone multifunctions and then use these to…

A reflexive Banach space $X$ with a basis $(e_i)$ is constructed having the property that every monotone basis is block finitely representable in each block basis of $X$.

The category of Banach Lie-Poisson spaces is introduced and studied. It is shown that the category of W*-algebras can be considered as one of its subcategories. Examples and applications of Banach Lie-Poisson spaces to quantization and…

The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…

We prove that every AF-algebra is isomorphic to a crossed product of a commutative AF-algebra by a partial automorphism. The case of UHF-algebras is treated in detail.

In this paper, we obtain formulas for the number of representations of positive integers as sums of arbitrarily many squares (and other polygonal numbers) with a certain natural weighting. The resulting weighted sums give Fourier…

Let $X$ be a perfect, compact subset of the complex plane. We consider algebras of those functions on $X$ which satisfy a generalised notion of differentiability, which we call $\mathcal{F}$-differentiability. In particular, we investigate…

A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…