Related papers: Equivalence of multi-norms
Dales and Polyakov introduced a multi-norm $\left( \left\|\cdot\right\|_n^{(2,2)}:n\in\mathbb{N}\right)$ based on a Banach space $\mathscr{X}$ and showed that it is equal with the Hilbert-multi-norm $\left(…
Analogues of Kolmogorov comparison theorems and some of their applications were established.
The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi- linear operators. In the present paper we push this subject further, by proving…
This is an extended version of my Nobel Lecture, delivered on December $8^{th}$ 2021. I will recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe my contribution to the development of this…
The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as `duality' is understood in physics and (ii) equivalence of theories, as `equivalence' is understood in logic and philosophy. The…
We present a formula for the class number of a multinorm one torus $T_{L/k}$ associated to any \'etale algebra $L$ over a global field $k$. This is deduced from a formula for analogues of invariants introduced by T.~Ono, which are…
The concept of conformally equivariant quantizations was introduced by Duval, Lecomte and Ovsienko in \cite{DLO} for manifolds endowed with flat conformal structures. They obtained results of existence and uniqueness (up to normalization)…
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate…
We summarize researches - in great deal jointly with my host Y. Sarantopoulos and his PhD. students V. Anagnostopoulos and A. Pappas - started by a Marie Curie fellowship in 2001 and is still continuing. The project was to study…
Univalence was first defined in the setting of homotopy type theory by Voevodsky, who also (along with Kapulkin and Lumsdaine) adapted it to a model categorical setting, which was subsequently generalized to locally Cartesian closed…
Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…
In this paper we develop a novel bootstrap test for the comparison of two multinomial distributions. The two distributions are called {\it equivalent} or {\it similar} if a norm of the difference between the class probabilities is smaller…
We show that (k,m)-linear mappings, introduced by I. Chernega and A. Zagorodnyuk in [3], are particular cases of polynomials. As corollaries, we expose some apparently overlooked properties in the literature. For instance, every multilinear…
Replacing the triangle inequality, in the definition of a norm, by $|x + y| ^{q}\leq 2^{q-1}(|x| ^{q} + |y| ^{q}) $, we introduce the notion of a q-norm. We establish that every q-norm is a norm in the usual sense, and that the converse is…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of exchangeable pairs for multivariate normal…
In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.
In the paper we consider the notion of hyper-quasi-identities and hyperquasivarieties as a generalization of the concept of quasi-identity and quasivariety invented by A. I. Mal'cev.
The main purpose of this paper is to develop some methods to investigate equivalent norms and Hardy-Littlewood type Theorems on Lipschitz type spaces of analytic functions and complex-valued harmonic functions. Initially, some…
A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.