Functional Mellin Transforms

2013/08/05 by J. LaChapelle, LaChapelle, J. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1308.1063

Expanded and re-posted to the ArXiv as two separate papers titled "A Proposed Definition of Functional Integrals" and "Exploring Functional Mellin Transforms"

openalex publication_date 2013/08/05 · arxiv created 2015/01/07 · arxiv updated 2015/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows a construction of functional Mellin transforms. In turn, the functional Mellin transforms can be used to define functional traces, logarithms, and determinants. The associated functional integrals are useful tools for probing function spaces in general and C^∗-algebras in particular. Several interesting aspects are explored.

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• Apparent Geometry from the Quantum Mechanics of Sp(8,ℂ)
• Functional Mellin and Zeta Zeros

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