کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9518167 | 1345530 | 2005 | 36 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Fourier transformation of Sato's hyperfunctions
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A new generalized function space in which all Gelfand-Shilov classes Sαâ²0 (α>1) of analytic functionals are embedded is introduced. This space of ultrafunctionals does not possess a natural nontrivial topology and cannot be obtained via duality from any test function space. A canonical isomorphism between the spaces of hyperfunctions and ultrafunctionals on Rk is constructed that extends the Fourier transformation of Roumieu-type ultradistributions and is naturally interpreted as the Fourier transformation of hyperfunctions. The notion of carrier cone that replaces the notion of support of a generalized function for ultrafunctionals is proposed. A Paley-Wiener-Schwartz-type theorem describing the Laplace transformation of ultrafunctionals carried by proper convex closed cones is obtained and the connection between the Laplace and Fourier transformations is established.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 196, Issue 2, 1 October 2005, Pages 310-345
Journal: Advances in Mathematics - Volume 196, Issue 2, 1 October 2005, Pages 310-345
نویسندگان
A.G. Smirnov,