Partial Cosine-Funk Transforms at Poles of the Cosine-λ Transform on Grassmann Manifolds

<p>The cosine-&#955; transform, denoted C^&#955;, 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-&#955; transform on the sphere, which is also a symmetric space. </p> <p> The family C^&#955; extends meromorphically in &#955; to the complex plane with poles at (among other values) &#955; =-1,…, -p. In this dissertation we normalize C^&#955; 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 <em>partial</em> cosine-Funk transforms. The transform that arises at &#955; = -p is the natural Funk transform for the Grassmannians, which was introduced by B. Rubin.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2015

Author dc:creator

• Cross, Christopher Adam

• integral transforms
• harmonic analysis
• Cλ transform

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-07072015-194931
https://repository.lsu.edu/gradschool_dissertations/748

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1747