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math.AP2019
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…
math.FA2019★ 1 cited
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.
math.CA2019★ 1 cited
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.