FOURIER AND CAUCHY–STIELTJES TRANSFORMS OF POWER LAWS INCLUDING STABLE DISTRIBUTIONS

DOI10.1142/S0129167X12500413zbMath1237.60015arXiv1107.3874OpenAlexW2963708041MaRDI QIDQ5389538

Takahiro Hasebe

Publication date: 21 April 2012

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3874

zbMATH Keywords

Fourier transformDiophantine approximationstable distributionnoncommutative probabilityCauchy-Stieltjes transform

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Free probability and free operator algebras (46L54) Power series (including lacunary series) in one complex variable (30B10) Noncommutative probability and statistics (46L53)

Cites Work

• On extrema of stable processes
• A convergent series representation for the density of the supremum of a stable process
• Strict limit types for monotone convolution
• Addition of freely independent random variables
• Stable laws and domains of attraction in free probability theory
• MONOTONE CONVOLUTION AND MONOTONE INFINITE DIVISIBILITY FROM COMPLEX ANALYTIC VIEWPOINT
• MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS
• Statistical-Mechanical Foundation of the Ubiquity of Lévy Distributions in Nature
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