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We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include $u ₙ + u_{\infty}$ where uₙ and $u_{\infty}$ are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form $S_{α} + i S_{β}$ where $S_{α}$ and $S_{β}$ are free semicircular elements of variance α and β.

Concentration functions in locally compact groups.

G. Willis, W. Jaworski, J. Rosenblatt (1996)

Mathematische Annalen

Continuous automorphism groups on a locally compact group contracting modulo a compact subgroup and applications to stable convolution semigroups.

W. Hazod, E. Siebert (1986)

Semigroup forum

Continuous Convolution Semigroups Integrating a Submultiplicative Function.

Eberhard Siebert (1982)

Manuscripta mathematica

Continuous measures and analytic sets

R. Kaufman (1989)

Colloquium Mathematicae

Continuous measures on compact Lie groups

M. Anoussis, A. Bisbas (2000)

Annales de l'institut Fourier

We study continuous measures on a compact semisimple Lie group $G$ using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on $G$ which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if $C$ is a compact set of continuous measures on $G$ there exists a singular measure $ν$ such that $ν * μ$ is absolutely continuous with respect to the Haar measure on...

Convolution de mesures portées par une surface convexe

Michel Talagrand (1974/1975)

Séminaire Choquet. Initiation à l'analyse

Convolution of singular measures

Raouf Doss (1973)

Studia Mathematica

Convolution Semigroups and Resolvent Families of Measures on Hypergroups.

Herbert Heyer, Walter R. Bloom (1984/1985)

Mathematische Zeitschrift

Convolutions of probability measures on semigroups.

F. Kinzl (1980)

Semigroup forum

Correction to the paper "Some problems and remarks on relative multipliers''

S. Hartman (1989)

Colloquium Mathematicae

Corrigendum and addendum to "A generalization of Wiener's criteria for the continuity of a Borel measure"

J. Belley, P. Morales (1984)

Studia Mathematica

Critical constants for recurrence of random walks on $G$ -spaces

Anna Erschler (2005)

Annales de l’institut Fourier

We introduce the notion of a critical constant $c_{r t}$ for recurrence of random walks on $G$ -spaces. For a subgroup $H$ of a finitely generated group $G$ the critical constant is an asymptotic invariant of the quotient $G$ -space $G / H$ . We show that for any infinite $G$ -space $c_{r t} \geq 1 / 2$ . We say that $G / H$ is very small if $c_{r t} < 1$ . For a normal subgroup $H$ the quotient space $G / H$ is very small if and only if it is finite. However, we give examples of infinite very small $G$ -spaces. We show also that critical constants for recurrence can be used...

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