Department
Home Page
About Us:
• Contact Info.
• Faculty
• Staff
• Students
Academic Program:
• Admission
• Undergraduate
• Graduate
• Certificates
Courses:
• Course Description
• Class Web Pages
• Class Syllabi
• Skills Tests
Research:
• Research Groups
• Colloquium
• Seminars
• News
Links:
| • Alumni Questionnaire |
| • Math Lab |
| • CAPA & Skills Tests |
| •Math Placement Test |
| • UCF Math Club |
| • Academic System Lab |
| • Careers |
| • American Mathematical Society |
| • Mathematical Association of America |
03/025/02 Colloquium
DR. DAVID R. LARSON
Texas A & M University
Texas A & M University
WAVELETS, FRAMES AND OPERATOR THEORY
Abstract: Orthonomal wavelets can be regarded as complete wandering vectors for a system of unitary operators acting on a separable infinite dimensional Hilbert space. We describe a method of constructing new wavelets by interpolating between known pairs of wavelets, and more generally interpolating over finite families of wavelets, using Hilbert space operator techniques. These considerations lead naturally to some basic global results for orthonormal wavelets, Riesz wavelets and frame wavelets that can tend to be surprising from a purely function-theoretic point of view. Included is the concept of a super-wavelet (a wavelet for a super-space), which has potential applications to multiplexing problems, and we give some new examples of sueprwavelets. These considerations also yield alternate derivations of some well-know function-theoretic results. Similar techniques can be applied to the windowed Fourier transforms found in Gabor Theory, or Weyl-Heisenberg Frame Theory, and we obtain some global density and connectivity results for these classes.