相关论文: Some Remarks on Vector-Valued Integration

A general method for analytic inversion of geometric integral transforms is proposed

Research in machine learning has polarized into two general approaches for regression tasks: Transductive methods construct estimates directly from available data but are usually problem unspecific. Inductive methods can be much more…

We focus on measurability and integrability for set valued functions in non-necessarily separable Fr\'echet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide…

The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…

We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields…

We present a survey of the theory of $\gamma$-radonifying operators and their applications to stochastic integration in Banach spaces.

We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.

The non-Archimedean spectral theory and spectral integration is developed. The analog of the Stone theorem is proved. Applications are considered for algebras of operators.

Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…

We introduce the class of vector measures of bounded $\gamma$-variation and study its relationship with vector-valued stochastic integrals with respect to Brownian motions.

In this paper we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory we present full statements of the iterated contraction principle and the Banach contraction principle in cone…

We introduce a notion of p-rough integrator on any Banach manifolds, for any $p\geq 1$, which plays the role of weak geometric Holder p-rough paths in the usual Banach space setting. The awaited results on rough differential equations…

Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

We define the $k$:th moment of a Banach space valued random variable as the expectation of its $k$:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective…

We are interested in Beurling spectrum of $\mathbb X-$valued functions with application in functional delay differential equations.

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…

An introduction to geometric valuation theory is given. The focus is on classification results for $\operatorname{SL}(n)$ invariant and rigid motion invariant valuations on convex bodies and on convex functions.

In analogy to valued fields, we study model-theoretic properties of valued vector spaces with variable base field by proving transfer principles down to the skeleton and down to the value set and base field. For instance, we give a formula…