相关论文: On summability, multipliability, product integrabi…
We derive Onsager-Machlup functionals for countable product measures on weighted $\ell^p$ subspaces of the sequence space $\mathbb{R}^{\mathbb{N}}$. Each measure in the product is a shifted and scaled copy of a reference probability measure…
This paper is a survey of a new family of Banach spaces ${KS}^2$ and $SD^2$ that provide the same structure for the Henstock-Kurzweil (HK) integrable functions as the $L^p$ spaces provide for the Lebesgue integrable functions. These spaces…
We establish that the summability of the series $\sum\varepsilon_n$ is the necessary and sufficient criterion ensuring that every $(1+\varepsilon_n)$ Markushevich basis in a separable Hilbert space is a Riesz basis. Further we show that if…
We develop the foundations of effective ultraproducts of fields and their Galois groups using the methods of computability theory. These computability-theoretic analogs of ultraproducts are called cohesive products, since the role of an…
Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower…
We first summarize joint work on several preliminary canonical Lambert series factorization theorems. Within this article we establish new analogs to these original factorization theorems which characterize two specific primary cases of the…
We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating…
We prove that the faithful and uniqueness of norm properties are stable in different product algebras such as direct-sum product algebra, convolution product algebra, and module product algebra. Further, we exhibit that these properties are…
We prove a substantial extension of a well-known result due to Bennett and Carl: The inclusion of a 2-concave symmetric Banach sequence space E into l_2 is (E,1)-summing, i.e. for every unconditionally summable sequence (x_n) in E the…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…
In analysis, it's often useful to know the value of a function at infinity, this operation possesses pleasant properties. However, even when the limit does not exist, some intuitive considerations may suggest that the function still assumes…
In this paper we prove a plenty of new results concerning summabililty properties of multilinear mappings between Banach spaces, such as an extension of Littlewood's 4/3 Theorem. Among other features, it is shown that every continuous…
We present an approach to cohomological dimension theory based on infinite symmetric products and on the general theory of dimension called the extension dimension. The notion of the extension dimension $\ExD(X)$ was introduced by…
We describe certain special consequences of certain elementary methods from group theory for studying the algebraic complexity of matrix multiplication, as developed by H. Cohn, C. Umans et. al. in 2003 and 2005. The measure of complexity…
This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…
For linear random dynamical systems in a separable Banach space $X$, we derived a series of Krein-Rutman type Theorems with respect to co-invariant cone family with rank-$k$, which present a (quasi)-equivalence relation between the…
Integral equations of the form $$ x(t)=x(t_0)+\int_{t_0}^t d[A]\,x=f(t)-f(t_0)$$ are natural generalizations of systems of linear differential equations. Their main goal is that they admit solutions which need not be absolutely continuous.…
We prove that there exists essentially one {\it minimal} differential algebra of distributions $\A$, satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l'impossibilit\'e de la multiplication des…
The paper deals with extension of bounded bilinear maps$.$ It gives a necessary and sufficient condition for extending a bounded bilinear map on the Cartesian product of subspaces of Banach spaces$.$ This leads to a full characterization…