SU\G(𝔸)/K·U

Multiplicative monotonic convolution

Hari Bercovici

Type: Article

Publication Date: 2005-07-01

Citations: 34

DOI: https://doi.org/10.1215/ijm/1258138229

Abstract

We show that the monotonic independence introduced by Muraki can also be used to define a multiplicative convolution. We also find a method for the calculation of this convolution based on an appropriate form of the Cauchy transform. Finally, we discuss infinite divisibility in the multiplicative monotonic context.

Locations

  • Illinois Journal of Mathematics - View - PDF

Similar Works

Action Title Year Authors
+ Multiplicative Monotone Convolution 2004 Hari Bercovici
+ A REMARK ON MONOTONIC CONVOLUTION 2005 Hari Bercovici
+ Summation of multiplicative functions 1983 Б. М. Широков
+ Summation of multiplicative functions 2002 Марис Евгеньевич Чанга
+ Laplace transforms of multiply monotonic functions 1941 Norman N. Royall
+ PDF Chat Monotonicity of multiplicative functions 1979 Zbigniew Nowacki
+ Additive and Multiplicative Functions with Similar Global Behavior 2015 Jean-Marie De Koninck
Nicolas Doyon
+ PDF Chat The identical equations of the multiplicative function 1930 R. Vaidyanathaswamy
+ PDF Chat Non-divisibility of some multiplicative functions 1973 E. J. Scourfield
+ PDF Chat Some remarks about additive and multiplicative functions 1946 P. Erdős
+ Multiplicative functions with small increments. II 1990 K.‐H. Indlekofer
И. Катаи
+ PDF Chat Conditionally Monotone Independence II: Multiplicative Convolutions and Infinite Divisibility 2011 Takahiro Hasebe
+ Multiplicative functions with small increments. III 1991 K.‐H. Indlekofer
И. Катаи
+ Omega theorems for the iterated additive convolution of a nonnegative arithmetic function 1981 Elmer K. Hayashi
+ Multiplicative functions 1984 Władysław Narkiewicz
+ Multiplicative monotone convolutions 2006 Uwe Franz
+ Multiplicative functions with small increments. I 1990 K.‐H. Indlekofer
И. Катаи
+ PDF Chat Divisibility properties of a class of multiplicative functions 1967 Władysław Narkiewicz
+ Multiplicative Functions 2003 Svetoslav Savchev
Titu Andreescu
+ Conditionally monotone independence II: Multiplicative convolutions and infinite divisibility 2009 Takahiro Hasebe

Works That Cite This (34)

Action Title Year Authors
+ PDF Chat Monotone increment processes, classical Markov processes, and Loewner chains 2020 Uwe Franz
Takahiro Hasebe
Sebastian Schleißinger
+ PDF Chat Limit Theorems for Monotonic Convolution and the Chernoff Product Formula 2013 Michael Anshelevich
John D. Williams
+ A combinatorial approach to monotonic independence over a C*-algebra 2006 Mihai Popa
+ PDF Chat A combinatorial approach to monotonic independence over a C<sup>∗</sup>-algebra 2008 Mihai Popa
+ Classical Scale Mixtures of Boolean Stable Laws 2014 Octavio Arizmend
Takahiro Hasebe
+ Independences and partial $R$-transforms in bi-free probability 2016 Paul Skoufranis
+ PDF Chat Haar states and Lévy processes on the unitary dual group 2016 Guillaume Cébron
Michaël Ulrich
+ PDF Chat Monotone convolution semigroups 2010 Takahiro Hasebe
+ PDF Chat The Exponential Map in Non-commutative Probability 2016 Michael Anshelevich
Octavio Arizmendi
+ PDF Chat CONDITIONALLY MONOTONE INDEPENDENCE I: INDEPENDENCE, ADDITIVE CONVOLUTIONS AND RELATED CONVOLUTIONS 2011 Takahiro Hasebe

Works Cited by This (4)

Action Title Year Authors
+ PDF Chat Semigroups of analytic functions and composition operators. 1978 Earl Berkson
Horaçio Porta
+ Addition of certain non-commuting random variables 1986 Dan Voiculescu
+ A REMARK ON MONOTONIC CONVOLUTION 2005 Hari Bercovici
+ MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS 2001 Naofumi Muraki