کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4616807 1339359 2013 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Distributions in spaces with thick points
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Distributions in spaces with thick points
چکیده انگلیسی

We present a theory of distributions in a space with a thick point in dimensions n≥2, generalizing the theory of thick distributions in one variable given in Estrada and Fulling (2007) [8]. The higher dimensional situation is quite different from the one dimensional case.We construct topological vector spaces of thick test functions and, by duality, spaces of thick distributions. We study several operations on these distributions, both algebraic and analytic, particularly partial differentiation. We introduce the notion of thick delta functions at the special point, not only of order 0 but of any integral order. We also consider the thick distributions constructed by the Hadamard finite part procedure. We give formulas for the derivatives of important thick distributions, including the finite part of power functions. We obtain the new formula ∂∗2Pf(r−1)∂xi∂xj=(3xixj−δijr2)Pf(r−5)+4π(δij−4ninj)δ∗ for the second order thick derivatives of the finite part of r−1 in R3, where δ∗δ∗ is a thick delta of order 0.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 401, Issue 2, 15 May 2013, Pages 821–835
نویسندگان
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