Toward a general theory of transmutation
A. Boumenir (K.F.U.P.M, Dhahran, Saudi Arabia, visiting University of, Illinois), and R. Carroll (Mathematics Dept., University of Illinois, Urbana)
TL;DR
This paper develops a comprehensive framework for transmutation operators applicable to selfadjoint operators within Gelfand triples, establishing key theorems on eigenfunction analyticity and Paley-Wiener properties.
Contribution
It introduces a general construction method for transmutation operators and proves foundational theorems on eigenfunction analyticity and spectral properties.
Findings
Established a general construction of transmutation operators.
Proved theorems on analyticity of generalized eigenfunctions.
Demonstrated Paley-Wiener type properties for the operators.
Abstract
A general construction of transmutation operators is developed for selfadjoint operators in Gelfand triples. Theorems regarding analyticity of generalized eigenfunctions and Paley-Wiener properties are proved.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Algebraic and Geometric Analysis · Quantum Mechanics and Applications