In the following paper, we provide a stochastic analogue to work of Shea and Wainger by showing that when the measure and state-independent diffusion coefficient of a linear Itô–Volterra equation are in appropriate Lp– weighted spaces, the solution lies in a weighted Lp–space in both an almost sure and moment sense.

The paper provides topological characterization for solution sets of differential inclusions with (not necessarily smooth) functional constraints in Banach spaces. The corresponding compactness and tangency conditions for the right hand-side are expressed in terms of the measure of noncompactness and the Clarke generalized gradient, respectively. The consequences of the obtained result generali...

* Work supported by the Office of Ordnance Research, United States Army, Contract No. DA-36-034-ORD-1296. 1 W. Feller, "The General Diffusion Operator and Positivity-preserving Semi-groups in One Dimension," Ann. Math., 60, 417-436, 1954; "The Parabolic Differential Equations and the Associated Semni-groups of Transformations," ibid., 55, 468-519, 1952; J. L. Doob, Stochastic Processes (New Yor...

We summarize the results on the differential geometric structure of Alexandrov spaces developed in [Otsu and Shioya 1994; Otsu 1995; Otsu and Tanoue a]. We discuss Riemannian and second differentiable structure and Jacobi fields on Alexandrov spaces of curvature bounded below or above.

It is known that a Fréchet space F can be realized as a projective limit of a sequence of Banach spaces Ei. The space Kc(F) of all compact, convex subsets of a Fréchet space, F, is realized as a projective limit of the semilinear metric spacesKc(E). Using the notion of Hukuhara derivative for maps with values inKc(F), we prove the local and global existence theorems for an initial value problem...

Differential modules are modules over rings of linear (partial) differential operators which are finite-dimensional vector spaces. We present a generalization of the Beke-Schlesinger algorithm that factors differential modules. The method requires solving only one set of associated equations for each degree d of a potential factor. Mathematics Subject Classification (2000). 13N05; 13N10; 13N15;...

A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason’s treatment of the general reductive case and the special nonreductive case of the space of horocycles. As a final application the differential operators on (not a priori reductive) isotropic pseudo-Riemannian spaces are cha...

This is an introduction to the subject of the differential topology of the space of smooth loops in a finite dimensional manifold. It began as background notes to a series of seminars given at NTNU and subsequently at Sheffield. The topics covered are: the smooth structure of the space of smooth loops; constructions involving vector bundles; submanifolds and tubular neighbourhoods; and a short ...

This paper is devoted to study the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Mönch’s fixed point theorem and the technique of measures of noncompactness.

We develop a GL qp (2) invariant differential calculus on a two-dimensional noncommutative quantum space. Here the coordinate space for the exterior quantum plane is spanned by the differentials that are commutative (bosonic) in nature.