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Distributionally regulated functions

Jasson Vindas, Ricardo Estrada (2007)

Studia Mathematica

We study the class of distributions in one variable that have distributional lateral limits at every point, but which have no Dirac delta functions or derivatives at any point, the "distributionally regulated functions." We also consider the related class where Dirac delta functions are allowed. We prove several results on the boundary behavior of functions of two variables F(x,y), x ∈ ℝ, y>0, with F(x,0⁺) = f(x) distributionally, both near points where the distributional point value exists and...

Distributions that are functions

Ricardo Estrada (2010)

Banach Center Publications

It is well-known that any locally Lebesgue integrable function generates a unique distribution, a so-called regular distribution. It is also well-known that many non-integrable functions can be regularized to give distributions, but in general not in a unique fashion. What is not so well-known is that to many distributions one can associate an ordinary function, the function that assigns the distributional point value of the distribution at each point where the value exists, and that in many cases...

Ditkin sets in homogeneous spaces

Krishnan Parthasarathy, Nageswaran Shravan Kumar (2011)

Studia Mathematica

Ditkin sets for the Fourier algebra A(G/K), where K is a compact subgroup of a locally compact group G, are studied. The main results discussed are injection theorems, direct image theorems and the relation between Ditkin sets and operator Ditkin sets and, in the compact case, the inverse projection theorem for strong Ditkin sets and the relation between strong Ditkin sets for the Fourier algebra and the Varopoulos algebra. Results on unions of Ditkin sets and on tensor products are also given.

Division and extension in weighted Bergman-Sobolev spaces.

Joaquín M. Ortega, Joan Fàbrega (1992)

Publicacions Matemàtiques

Let D be a bounded strictly pseudoconvex domain of Cn with C ∞ boundary and Y = {z; u1(z) = ... = ul(z) = 0} a holomorphic submanifold in the neighbourhood of D', of codimension l and transversal to the boundary of D.In this work we give a decomposition formula f = u1f1 + ... + ulfl for functions f of the Bergman-Sobolev space vanishing on M = Y ∩ D. Also we give necessary and sufficient conditions on a set of holomorphic functions {fα}|α|≤m on M, so that there exists a holomorphic function in the...

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