Degree Type

Creative Component

Semester of Graduation

Spring 2021

Department

Mathematics

First Major Professor

Joseph Iverson

Degree(s)

Master of Science (MS)

Major(s)

Mathematics

Abstract

For a second countable locally compact Hausdorff abelian group G and discrete closed subgroup H where G/H is compact, it is possible to characterize subspaces of L2 (G) which are invariant under translation of H. Prior to this work, these characterizations were extended by lifting the requirements that H is discrete and G/H is compact. We verify the older results in the case of Rn and Z n and state the generalized case when G is an LCA group and H has the former requirements stated above. Then using these results, we characterize subspaces of R/Z that invariant under {0, 1 2 } and extend the characterization to n dimensions, giving results with generalized even and odd functions.

Copyright Owner

Berner Chad

File Format

PDF

Embargo Period (admin only)

4-21-2021

1

Included in

Analysis Commons

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