Identifier

etd-07072015-194931

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

The cosine-λ transform, denoted Cλ, is a family of integral transforms we can define on the sphere and on the Grassmannian manifolds of p-dimensional subspaces in Kn where K is R, C or the skew field H of quaternions. We treat the Grassmannians as the symmetric spaces SO(n)/S(O(p) × O(q)), SU(n)/S(U(p) × U(q)) and Sp(n)/(Sp(p) × Sp(q)) and we work by analogy with the case of the cosine-λ transform on the sphere, which is also a symmetric space.

The family Cλ extends meromorphically in λ to the complex plane with poles at (among other values) λ =-1,…, -p. In this dissertation we normalize Cλ and we use well known harmonic analysis tools to evaluate at those poles. The result is a series of integral transforms on the Grassmannians that we can view as partial cosine-Funk transforms. The transform that arises at λ = -p is the natural Funk transform for the Grassmannians, which was introduced by B. Rubin.

Date

2015

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Olafsson, Gestur

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