Translation Invariant Positive Definite Hermitian Bilinear Ultradistributions |
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Authors: | Cho Jonggyu |
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Institution: | (1) Department of Mathematics, Seoul National University, Seoul, 151–742, Korea E-mail: Email |
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Abstract: | Every translation invariant positive definite Hermitian bilinear functional on the Gel'fand-Shilov space sMpMp( n×nK) of general type S is of the form B( , ) = ![int](/content/h0464808028g0242/xxlarge8747.gif) (x) (x)d (x), , sMpMp ( n), where is a positive {M}-tempered measure, i.e., for every > 0 exp-M( |x|)] d (x) < . To prove this we prove Schwartz kernel theorem for {M}-tempered ultradistributions and need Bochner-Schwartz theorem for {M}-tempered ultradistributions. Our result includes most of the quasianalytic cases. Also, we obtain parallel results for the case of Beurling type (Mp. |
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Keywords: | Schwartz kernel theorem translation invariant positive definite Hermitian bilinearfunctional ultradistribution |
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