The $L^2$-index theorem for homogeneous spaces

Tb-theorem on non-homogeneous spaces

0 Introduction: main objects and results 3 0.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0.2 An application of T1-heorem: electric intensity capacity . . . . . . . . . . . . 7 0.3 How to interpret Calderón–Zygmund operator T? . . . . . . . . . . . . . . . 9 0.3.1 Bilinear form is defined on Lipschitz functions . . . . . . . . . . . . . 10 0.3.2 Bilin...

L2-index Theorem for Elliptic Differential Boundary Problems

Suppose M is a compact manifold with boundary ∂M . Let M̃ be a normal covering of M . Suppose (A, T ) is an elliptic differential boundary value problem on M with lift (Ã, T̃ ) to M̃ . Then the von Neumann dimension of kernel and cokernel of this lift are defined. The main result of this paper is: These numbers are finite, and their difference, by definition the von Neumann index of (Ã, T̃ ), equal...

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

Vector ultrametric spaces and a fixed point theorem for correspondences

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.