Stevan Pilipovic

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We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth hypoelliptic symbols. Methodological novelties and technical refinements appear embedded into classical strategies of(More)
A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ul-tra(pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac's delta distribution induces discrete topology on the basic(More)
Number of pages: 140 pages Thank you for reading boundary values and convolution in ultradistribution spaces. Maybe you have knowledge that, people have search numerous times for their favorite readings like this boundary values and convolution in ultradistribution spaces, but end up in infectious downloads. Rather than enjoying a good book with a cup of(More)
We study localization operators within the framework of ultra-distributions. More precisely, given a symbol a and two windows ϕ1, ϕ2, we investigate the multilinear mapping from (a, ϕ1, ϕ2) ∈ S (1) (R 2d) × S (1) (R d) × S (1) (R d) to the localization operator A ϕ 1 ,ϕ 2 a. Results are formulated in terms of modulation spaces with weights which may have(More)
In a recent paper, we gave a topological description of Colombeau type algebras introducing algebras of sequences with exponential weights. Embeddings of Schwartz spaces into the Colombeau algebra G are well known, but for ultradistribution and periodic hyperfunction type spaces we give new constructions. We show that the multiplication of regular enough(More)
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove functorial properties of those algebras and show how weak equalities, in the sense of various associations, can be described in(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract We study parabolic stochastic partial differential equations (SPDEs), driven by two types of operators: one linear closed operator generating a C0−semigroup and one linear bounded operator with Wick-type multiplication, all of them set in the infinite dimensional space framework of white noise(More)