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Semigroups related to additive and multiplicative, free and Boolean convolutions

Octavio Arizmendi, Takahiro Hasebe (2013)

Studia Mathematica

Belinschi and Nica introduced a composition semigroup of maps on the set of probability measures. Using this semigroup, they introduced a free divisibility indicator, from which one can know quantitatively if a measure is freely infinitely divisible or not. In the first half of the paper, we further investigate this indicator: we calculate how the indicator changes with respect to free and Boolean powers; we prove that free and Boolean 1/2-stable laws have free divisibility indicators equal to infinity;...

Sequences of differential operators: exponentials, hypercyclicity and equicontinuity

L. Bernal-González, J. A. Prado-Tendero (2001)

Annales Polonici Mathematici

An eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new sufficient conditions for a sequence of infinite order linear differential operators to be hypercyclic on the space of holomorphic functions on certain domains of ℂ N are shown. Moreover, several necessary conditions are furnished. The equicontinuity of a family of operators as above is also studied, and it is characterized if the domain is ℂ N . The results obtained extend or improve earlier work...

Series in Mittag-Leffler Functions: Inequalities and Convergent Theorems

Paneva-Konovska, Jordanka (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 30A10, 30B10, 30B30, 30B50, 30D15, 33E12In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we prove Cauchy-Hadamard, Abel, Tauber and Littlewood type theorems. Asymptotic formulae are also provided for the Mittag-Leffler functions in the case of " values of indices that are used in the proofs of the convergence theorems for the considered series.

Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions

Paweł Domański, Mikael Lindström (2002)

Annales Polonici Mathematici

We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.

Sharp bounds for the intersection of nodal lines with certain curves

Junehyuk Jung (2014)

Journal of the European Mathematical Society

Let Y be a hyperbolic surface and let φ be a Laplacian eigenfunction having eigenvalue - 1 / 4 - τ 2 with τ > 0 . Let N ( φ ) be the set of nodal lines of φ . For a fixed analytic curve γ of finite length, we study the number of intersections between N ( φ ) and γ in terms of τ . When Y is compact and γ a geodesic circle, or when Y has finite volume and γ is a closed horocycle, we prove that γ is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between N ( φ ) and γ is O ( τ ) . This bound is sharp.

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