When is a Riesz distribution a complex measure?
Copyright policy )When is a Riesz distribution a complex measure?
Let R_αbe the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by the complex number α. I give an elementary proof of the necessary and sufficient condition for R_αto be a locally finite complex measure (= complex Radon measure).
LaTeX2e, 15 pages. Version 2 contains some small changes suggested by a referee
- University College London United Kingdom
- UNIVERSITY COLLEGE LONDON, Bartlett School of Planning United Kingdom
- New York University United States
harmonic analysis on symmetric cones, Noncommutative Jordan algebras, symmetric cone, Laplace transform, Radon measure, locally finite, Mathematics - Statistics Theory, Statistics Theory (math.ST), Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), determinant, Operations with distributions and generalized functions, Harmonic analysis on homogeneous spaces, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Euclidean Jordan algebra, Representation Theory (math.RT), unitary representation, Integral operators, Riesz distribution, Wallach set, local Laplace transform, Gindikin's theorem, Mathematics - Classical Analysis and ODEs, 43A85 (Primary) 17A15, 17C99, 28C10, 44A10, 46F10, 47G10, 60E05, 62H05 (Secondary), positive definite orbit, Mathematics - Representation Theory
harmonic analysis on symmetric cones, Noncommutative Jordan algebras, symmetric cone, Laplace transform, Radon measure, locally finite, Mathematics - Statistics Theory, Statistics Theory (math.ST), Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), determinant, Operations with distributions and generalized functions, Harmonic analysis on homogeneous spaces, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Euclidean Jordan algebra, Representation Theory (math.RT), unitary representation, Integral operators, Riesz distribution, Wallach set, local Laplace transform, Gindikin's theorem, Mathematics - Classical Analysis and ODEs, 43A85 (Primary) 17A15, 17C99, 28C10, 44A10, 46F10, 47G10, 60E05, 62H05 (Secondary), positive definite orbit, Mathematics - Representation Theory
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