The main purpose of this paper is to use the idea of n-norm and a modulus function to construct some multiplier sequence spaces with base space X, a real linear n-norm space. We study the spaces for linearity, existence of paranorm, completeness and some inclusion properties involving these spaces. Mathematics Subject Classification: 40A05, 46A45, 46E30

Let X be a symmetric right process, and let Z = {Zt, t ≥ 0} be a multiplicative functional of X that is the product of a Girsanov transform, a Girsanov transform under time-reversal and a continuous Feynman-Kac transform. In this paper we derive necessary and sufficient conditions for the strong L-continuity of the semigroup {Tt, t ≥ 0} given by Ttf(x) = Ex [Ztf(Xt)], expressed in terms of the ...

Let {L x t ; (x, t) ∈ R 1 × R 1 + } denote the local time of Brownian motion, and α t := ∞ −∞ (L x t) 2 dx. Let η = N(0, 1) be independent of α t. For each fixed t, ∞ −∞ (L x+h t − L x t) 2 dx − 4ht h 3/2 L → 64 3 1/2 √ α t η as h → 0. Equivalently, ∞ −∞ (L x+1 t − L x t) 2 dx − 4t t 3/4 L → 64 3 1/2 √ α 1 η as t → ∞. 1. Introduction. In [10] almost sure limits are obtained for the L p moduli o...

Bǎrbosu and Muraru (2015) introduced the bivariate generalization of the q -Bernstein–Schurer–Stancu operators and constructed a GBS operator of q -Bernstein–Schurer–Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In...