Related papers: On summability, multipliability, product integrabi…
In this paper, we study the notion of mid summability in a general setting using the duality theory of sequence spaces. We define the vector valued sequence space $\lambda^{mid}(X)$ corresponding to a Banach space $X$ and sequence space…
The scientific and practical needs of the twenty-first century lead humankind to convergence of the specialized and diverse branches of science and technology. This convergence reveals the need for new mathematical theories capable of…
We present necessary and sufficient conditions to hold true a Kramer type sampling theorem over semi-inner product reproducing kernel Banach spaces. Under some sampling-type hypotheses over a sequence of functions on these Banach spaces it…
The system of undetermined coefficients of a bifurcation problem G[z]=0 in Banach spaces is investigated for proving the existence of families of solution curves by use of the implicit function theorem. The main theorem represents an…
We introduce a class of Banach algebras of generalized matrices and study the existence of approximate units, ideal structure, and derivations of them.
The purpose of this paper is to establish an injectivity theorem generalized to pseudo-effective line bundles with transcendental (non-algebraic) singular hermitian metrics and multiplier ideal sheaves. As an application, we obtain a Nadel…
In this paper we consider a family of multiple Hurwitz zeta values with bi-indices parameterized by $\mu$ with $\Ree(\mu)>0$. These values are equipped with both the $\mu$-stuffle product from their series definition and the shuffle product…
We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all…
In this paper the analogy between differential forms arising from integrals in additive calculus and forms arising from the integrals in product calculus is investigated. It is found that with an appropriate definition of scalar…
We employ a multivariate extension of the Gauss quadrature formula, originally due to Berens, Schmid and Xu [BSX95], so as to derive cubature rules for the integration of symmetric functions over hypercubes (or infinite limiting…
The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and…
Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales.
In this paper, we propose extensions for the classical Kummer test, which is a very far-reaching criterion that provides sufficient and necessary conditions for convergence and divergence of series of positive terms. Furthermore, we present…
We study the equational theory of the Weihrauch lattice with multiplication, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the product $\times$, and the finite…
We discuss pruning and coloring lemmas on regular families. We discuss several applications of these lemmas to computing the Szlenk index of certain $w^*$ compact subsets of the dual of a separable Banach space. Applications include…
In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions…
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…
Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…
A class of Schr\"odinger-type second-order linear differential equations with a large parameter $u$ is considered. Analytic solutions of this type of equations can be described via (divergent) formal series in descending powers of $u$.…
Let ${\mathcal A}$ and ${\frak A}$ be Banach algebras such that ${\mathcal A}$ is a Banach ${\frak A}$-bimodule with compatible actions. We define the product ${\cal A}\rtimes{\frak A}$, which is a strongly splitting Banach algebra…