Strongly Operator‐Decomposable Probability Measures on Separable Banach Spaces

Siebert, Eberhard

doi:10.1002/mana.19911540126

Cited by 8 publications

(9 citation statements)

References 13 publications

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“…The notion of T -decomposable measures on infinite-dimensional cases, mainly the Banach space situation was studied in [7], [20] and [21].…”

Section: Definitionmentioning

confidence: 99%

Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

Raja

2003

Monatsh. Math.

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T -semi-selfdecomposability, operator selfdecomposability and subclasses L m (b, (T t )) andL m (b, (T t )) of measures on complete separable metric vector spaces are introduced and basic properties are proved. In particular, we show that µ is T -semi-selfdecomposable if and only if µ = T (µ)ν where ν is infinitely divisible and µ is operator selfdecomposable if and only if µ ∈ L 0 (b, (T t )) for all 0 < b < 1.2000 Mathematics Subject Classification: 60B11, 60B12.

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“…The notion of T -decomposable measures on infinite-dimensional cases, mainly the Banach space situation was studied in [7], [20] and [21].…”

Section: Definitionmentioning

confidence: 99%

Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

Raja

2003

Monatsh. Math.

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“…On vector spaces (finite or infinite dimensional) strongly ρ-decomposable laws are called strongly operator-decomposable, see [11], [23], [24]. For the real line such laws were first studied in [16].…”

Section: This Is In Particular the Case Ifmentioning

confidence: 99%

Semistable Selfdecomposable Laws on Groups

Hazod¹,

Shah²

2001

Journal of Applied Analysis

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Abstract. The most prominent examples of (operator-) selfdecomposable laws on vector spaces are (operator-) stable laws. In the past (operator-) semistability -a natural generalisation -had been intensively investigated, hence the description of the intersection of the classes of semistable and selfdecomposable laws turned out to be a challenging problem, which was finally solved by A. Luczak's investigations [17].For probabilities on groups, in particular on simply connected nilpotent Lie groups there exists meanwhile a satisfying theory of decomposability and semistability. Consequently it is possible to obtain a description of the intersection of these classes of measures -under additional commutativity assumptions -leading finally to partial extensions of the above-mentioned results for vector spaces to the group case.1991 Mathematics Subject Classification. 60B15, 60E07, 60F05, 43A05.

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“…In analogy to the Urbanik classes in the case of self-decomposability, nested classes of multiple operator decomposable laws and their properties were investigated. For the background the reader is referred e.g., to [12], [31], [32] for finite and infinite dimensional real vector spaces, and [16] and the references therein for multiple decomposability. In case of locally compact groups we mention R. Shah [27], Raja [23], see also [6], and for multiple decomposability on p-adic groups and vector spaces, [18] and the literature mentioned there.…”

Section: Introductionmentioning

confidence: 99%

Multiple decomposability of probabilities on contractible locally compact groups

Hazod

Kosfeld

2013

Proc Math Sci

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Abstract. Operator decomposable probabilities on vector spaces -generalizing (semi-)stable and self-decomposable laws -are well known. More specific concepts, multiple operator decomposable laws, generalizing the nested Urbanik classes in the case of selfdecomposability, were investigated in fundamental papers by Maejima et al. [16], [17] resp. by Maejima and R. Shah [18] for real resp. p-adic vector spaces. For locally compact groups, decomposability properties were studied by R. Shah [27], Raja [23], see also [6]. Here we are concerned with multiple decomposability on locally compact groups and generalize -as far as possible -the results in [16], [18]. In fact, as it turned out that contraction properties play an essential role, hence throughout we concentrate on contractible locally compact groups.

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Strongly Operator‐Decomposable Probability Measures on Separable Banach Spaces

Cited by 8 publications

References 13 publications

Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

Semistable Selfdecomposable Laws on Groups

Multiple decomposability of probabilities on contractible locally compact groups

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