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C. R. E. Raja

Publications and source records attributed to C. R. E. Raja.

25 records · Page 2Linked to original sources
arXiv2003

Operator semi-selfdecomposable measures and related nested subclasses of measures on vector spaces

$T$-semi-selfdecomposability and subclasses $L_m(b, Q)$ and $\tilde L_m(b, Q)$ 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 $μ\in L_0(b, Q)$ for all $0< b < 1$.

math.PR↗
arXiv2003

On heredity of strongly proximal actions

We prove that action of a semigroup T on compact metric space X by continuous selfmaps is strongly proximal if and only if T action on P(X), the space of probability measures on $X$ with weak topology, is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal.

math.DS↗
arXiv2002

Identity excluding groups

We consider the class of groups called identity excluding which has the property that any non-trivial irreducible unitary representation restricted to a dense subgroup does not weakly contain the trivial representation. For adapted and strictly aperiodic probability measures on these groups, it is known that the averages of unitary representations converge strongly. We show that motion group of a totally disconnected nilpotent group and certain class of p-adic algebraic groups which includes gruops whose solvable radical is type R are identity excluding. We also prove the convergence of averages of unitary representations for split solvable algebraic groups, which are not necessarily identity excluding.

math.RT↗
arXiv2002

Krengel-Lin decomposition for probability measures on hypergroups

A Markov operator $P$ on a $σ$-finite measure space $(X, Σ, m)$ with invariant measure $m$ is said to have Krengel-Lin decomposition if $L^2 (X) = E_0 \oplus L^2 (X,Σ_d)$ where $E_0 = \{f \in L^2 (X) \mid ||P^n (f) || \ra 0 \}$ and $Σ_d$ is the deterministic $σ$-field of $P$. We consider convolution operators and we show that a measure $\lam$ on a hypergroup has Krengel-Lin decomposition if and only if the sequence $(\check \lam ^n *\lam ^n)$ converges to an idempotent or $\lam$ is scattered. We verify this condition for probabilities on Tortrat groups, on commutative hypergroups and on central hypergroups. We give a counter-example to show that the decomposition is not true for measures on discrete hypergroups which is in contrast to the discrete groups case.

math.PR↗
arXiv2002

Absolute continuity of autophage measures on finite-dimensional vector spaces

We consider a class of measures called autophage which was introduced and studied by Szekely for measures on the real line. We show that the autophage measures on finite-dimensional vector spaces over real or p-adic field are infinitely divisible without idempotent factors and are absolutely continuous with bounded continuous density. We also show that certain semistable measures on such vector spaces are absolutely continuous.

math.PR↗