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Supports of convolutions of identical distributions

, 1967
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Convolution of temperate distributions

Publicationes Mathematicae Debrecen, 2022
Let \(L_ n\), \(n\in \mathbb N\), be the Hilbert space of all functions \(\phi:\mathbb R^ r\to \mathbb C\) for which each \(x^{\alpha}D^{\beta}\phi\), \(\alpha,\beta \in \mathbb N^ r\), \(| \alpha +\beta | \leq n\), is square integrable on \(\mathbb R^ r\) and \(L_{-n}\) be the dual space of \(L_ n\).
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Convolutions of Singular Distribution Functions

Ukrainian Mathematical Journal, 2004
The author constructs a new example of a sequence \(F_n\) of singular distributions, such that all finite convolutions \(F_1*F_2*\cdots *F_n\) (and even all finite convolutions containing distributions of transformed random variables \(\xi_k^i=\alpha_k^i\xi_k+\beta_k^i\), \(\alpha_k^i,\beta_k^i\in \mathbb R\), \(\alpha_k^i\neq 0\), where \(F_k ...
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Convolutions of α‐unimodal discrete distributions

Statistica Neerlandica, 1999
This note proves that the convolution of an α‐unimodal discrete distribution with a β‐unimodal discrete distribution is (α+β)‐unimodal whenever (α+β)≥1. This is the discrete analogue of the fundamental result on generalized unimodality given by Olshen and Savage (1970).
Wu, F., Dharmadhikari, S.
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Commutative convolution of functions and distributions

Integral Transforms and Special Functions, 2007
The commutative convolution f*g of two distributions f and g in 𝒟′ is defined as the limit of the sequence {(fτ n )* (gτ n )}, provided the limit exists, where {τ n } is a certain sequence of functions τ n in 𝒟 converging to 1. It is proved that for λ≠0,±1,±2, …, where B denotes the Beta function.
Brian Fisher, Kenan Taş
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Multimodal Convolutions of Unimodal Infinitely Divisible Distributions

Theory of Probability & Its Applications, 1995
Somewhat contrary to first intuition, convolutions of unimodal distributions need not be unimodal. The paper offers another example in this vein: a unimodal, infinitely divisible distribution \(\mu\) with the property that \(\mu*\mu\) is strictly \(n\)-modal, \(n\) a given finite integer.
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Approximation of convolutions of multidimensional distributions

Journal of Soviet Mathematics, 1987
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 142, 68-80 (Russian) (1985; Zbl 0566.60025).
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Convolution mixtures of infinitely divisible distributions

Mathematical Proceedings of the Cambridge Philosophical Society, 1981
AbstractA great deal is known about infinitely divisible distributions on [0, ∞). In this paper, a simple mapping which can be used to extend this information to more general convolution algebras is examined. Some examples are given where this approach has proved fruitful.
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On the Convolution of Distribution Functions

The American Mathematical Monthly, 1970
(1970). On the Convolution of Distribution Functions. The American Mathematical Monthly: Vol. 77, No. 7, pp. 745-746.
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On the Convolution of Scaled Sibuya Distributions

Sankhya A
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