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Extremal case of parabolic differential equations having discontinuous unbounded coefficients. Existence of fundamental solution for an initial Cauchy problem. Parametrix method
M. R. Formica, E. Ostrovsky, L. Sirota
We prove in this short report the existence of a fundamental solution (F.S.) for the Cauchy initial boundary problem on the whole space for the parabolic differential equation havi…
Central Limit Theorem in Lebesgue-Riesz spaces for weakly dependent random sequences
M. R. Formica, E. Ostrovsky, L. Sirota
We deduce sufficient conditions for the Central Limit Theorem (CLT) in the Lebesgue-Riesz space L(p) defined on some measure space for the sequence of centered random variables sat…
Fundamental solution for Cauchy initial value problem for parabolic PDEs with discontinuous unbounded first-order coefficient at the origin. Extension of the classical parametrix method
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous un…
Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We prove that the Grand Lebesgue Space, builded on a unimodular locally compact topological group, forms a Banach algebra relative to the convolution.
Asymptotic and non-asymptotic estimates for multivariate Laplace integrals
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.