Related papers: Generalized Lindemann-Weierstrass and Gelfond-Schn…

Gelfand - Na\u{i}mark theorem supplies a one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological space.…

The norm closure of the algebra generated by the set $\{n\mapsto {\lambda}^{n^k}:$ $\lambda\in{\mathbb {T}}$ and $k\in{\mathbb{N}}\}$ of functions on $({\mathbb {Z}}, +)$ was studied in \cite{S} (and was named as the Weyl algebra). In this…

We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will…

We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence. In fact we prove these theorems not only for…

A kind of generalized Gelfand pair is introduced via a Banach algebra consisting of bi-invariant functions in a weighted Lebesgue space. The related spherical functions and the Fourier transformation are constructed. The multipliers of the…

We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree polynomial, which we show is invariant of the dissection…

In the present paper, the authors introduce several new integral transforms including the Ln-transform, the L2n-transform and P2n-transform generalizations of the classical Laplace transform and the classical Stieltjes transform as…

We prove a formula for the structure sheaf of a quiver variety in the Grothendieck ring of its embedding variety. This formula generalizes and gives new expressions for Grothendieck polynomials. We furthermore conjecture that the…

In a recent work, Gun and co-workers have proposed that $\,\sum_{n=-\infty}^{\infty}{(n+\alpha)^{-k}}\,$ is a transcendental number for all integer $\,k$, $k > 1$, and $\,\alpha \in \mathbb{Q} \backslash \mathbb{Z}$. Here in this work, this…

The famous result of Lindemann and Weierstrass says that if $a_{1},a_{2},\ldots,a_{n}$ are distinct algebraic numbers, then $e^{a_{1}},e^{a_{2}},\ldots,e^{a_{n}}$ are linearly independent complex numbers over the field…

We apply recent knowledge and techniques of the new generalized upper and lower Legendre conjugates to the theory of weight functions in the sense of Braun-Meise-Taylor and study in detail the effects on the corresponding associated weight…

We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic…

We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this…

This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…

We present a discussion of generalized statistics based on Renyi's, Fisher's and Tsallis's measures of information. The unifying conceptual framework which we employ here is provided by information theory. Important applications of…

In this paper we combine methods from additive combinatorics and Diophantine geometry to study the generalised sum-product phenomenon in algebraic groups. As an application of this circle of ideas, we resolve a conjecture of Bremner on…

We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These…

We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effective method for computing Weierstrass functions, their…

Bliem and Kousidis (arXiv:1109.4624) recently considered a family of random variables whose distributions are given by the generalized Galois numbers (after normalization). We give probabilistic interpretations of these random variables,…

We study how to generate new Lie algebras $\mathcal{G}(N_0,..., N_p,...,N_n)$ from a given one $\mathcal{G}$. The (order by order) method consists in expanding its Maurer-Cartan one-forms in powers of a real parameter $\lambda$ which…