Positive-definite distributions and intertwining operators

Intertwining operators and residues II. Invariant distributions

1. Residues . ..... ........ .... ... .... 54 2. ir-discrete distributions ............... . .. . . .. . 58 3. Admissible families of operators .......... ............. 67 4. The main formula ............. ... ............ 74 5. Completion of the induction argument .................... 83 6. Cuspidal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7. Conclusions ..............

Positive definite distributions and normed spaces

We answer a question of Alex Koldobsky. We show that for each −∞< p < 2 and each n 3−p there is a normed space X of dimension n which embeds in Ls if and only if −n < s p. © 2011 Elsevier Inc. All rights reserved. MSC: 52A21

Intertwining Operators and Residues

Logarithmic Intertwining Operators and Vertex Operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1)a, of central charge 1 − 12a . We classify these operators in terms of depth and provide explicit constructions ...

Karcher Means and Karcher Equations of Positive Definite Operators

The Karcher or least-squares mean has recently become an important tool for the averaging and studying of positive definite matrices. In this paper we show that this mean extends, in its general weighted form, to the infinite-dimensional setting of positive operators on a Hilbert space and retains most of its attractive properties. The primary extension is via its characterization as the unique...