Introduction.-Let R,Y be the space of reals and a Banach space, respectively. The norm of elements in these spaces will be denoted by |. A nonempty family of sets V of an abstract space X will be called a pre-ring if for any two sets A,,A2a V we have Ai nA2G V, and there exist disjoint sets B1,..., BkEV such that A1\A2 = B1U ... UBt. A nonnegative finite-valued function v on the pre-ring V will...

In this talk we introduce and study quaternion-valued positive definite functions on locally compact Abelian groups, real countably Hilbertian nuclear spaces and on the space of countably infinite tuples of real numbers endowed with the Tychonoff topology. In particular, we prove a quaternionic version of the Bochner-Minlos theorem. We will see that in all these various settings the integral re...

The aim of the present paper is to study a Bochner Ricci semi-symmetric quasi-Einstein Hermitian manifold (QEH)n, a Bochner Ricci semi-symmetric generalised quasi-Einstein Hermitian manifold G(QEH)n and a Bochner Ricci semisymmetric pseudo generalised quasi-Einstein Hermitian manifold P (GQEH)n.

In this paper we are begining to explore the complex counterpart of the Chern-Simon-Witten theory. We define the complex analogue of the Gauss linking number for complex curves embedded in a Calabi-Yau threefold using the formal path integral that leads to a rigorous mathematical expression. We give an analytic and geometric interpretation of our holomorphic linking following the parallel with ...

This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are stu...

The purpose of this paper is to study the boundedness in the context of Triebel-Lizorkin spaces for some multilinear operators related to certain convolution operators. The operators include Littlewood-Paley operator, Marcinkiewicz integral, and Bochner-Riesz operator. 1. Introduction. Let T be a Calderon-Zygmund operator. A well-known result of Coif-man et al. [6] states that the commutator [b...

In this article we introduce the concept of second Φ-variation in the sense of Schramm for normed-space valued functions defined on an interval [a, b] ⊂ R. To that end we combine the notion of second variation due to de la Vallée Poussin and the concept of φ-variation in the sense of Schramm for real valued functions. In particular, when the normed space is complete we present a characterizatio...

This paper surveys and compares some recent approaches to stochastic infinite-dimensional geometry on the space Γ of configurations (i. e. locally finite subsets) of a Riemannian manifold M under Poisson measures. In particular, different approaches to Bochner– Weitzenböck formulas are considered. A unitary transform is also introduced by mapping functions of n configuration points to their mul...

Abstract In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented Neumann boundary conditions, when source term equation belongs a Lebesgue space, under various integrability regimes. Our method is based an integral refinement Bochner identity, and leads “semilinear Calderón...