REPRESENTATION AND ANALYSIS OF SIGNALS. PART XI. INTEGRAL TRANSFORMS AND TIME-VARYING SYSTEMS
Abstract
The objective of this dissertation is to examine the fundamental character of the transform method within the framework of the general theory of eigenfunction expansions for linear differential operators. It is shown that the existence of an integral transform which is compatible with a given system is dependent on the existence of a purely continuous spectrum for the canonical operator associated with that system. A heuristic development of the connection between spectral theory and integral transforms is presented. The theory and application of integral transforms for the systems with second-order canonical operators is developed. The dissertation concludes with a brief discussion of a generalization of the expansion theory to systems with higherorder canonical operators. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 21, 1962
- Accession Number
- AD0277013
Entities
People
- Leonard S Weiss
Organizations
- Johns Hopkins University