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The Heisenberg uncertainty relation in harmonic analysis on p -adic numbers field

Cui MinggenZhang Yanying — 2005

Annales mathématiques Blaise Pascal

In this paper, two important geometric concepts–grapical center and width, are introduced in p -adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in p -adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on p -adic numbers field.

Weyl-Heisenberg frame in p -adic analysis

Minggen CuiXueqin Lv — 2005

Annales mathématiques Blaise Pascal

In this paper, we establish an one-to-one mapping between complex-valued functions defined on R + { 0 } and complex-valued functions defined on p -adic number field Q p , and introduce the definition and method of Weyl-Heisenberg frame on hormonic analysis to p -adic anylysis.

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