Abstract

In the Dunkl setting, we establish three continuous uncertainty principles of concentration type, where the sets of concentration are not intervals. The first and the second uncertainty principles are Lp versions and depend on the sets of concentration T and W, and on the time function f. The time-limiting operators and the Dunkl integral operators play an important role to prove the main results presented in this paper. However, the third uncertainty principle is also Lp version depends on the sets of concentration and he is independent on the band limited function f. These uncertainty principles generalize the results obtained for the Fourier transform and the Dunkl transform in the case p=2.

Highlights

  • In the Dunkl setting, we establish three continuous uncertainty principles of concentration type, where the sets of concentration are not intervals

  • The author [9,10] proved a general forms of the Heisenberg-Pauli-Weyl inequality and he established a logarithmic uncertainty principle [11]

  • Based on the ideas of Donoho and Stark, we show a continuoustime uncertainty principle of concentration type

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Summary

Introduction

In the Dunkl setting, we establish three continuous uncertainty principles of concentration type, where the sets of concentration are not intervals. -concentrated to W in Lkp -norm, q = p/(p−1), if there is a function h(w) vanishing outside W with We prove another version of continuous-time uncertainty principle of concentration type for the L1k ∩ Lkp theory: If εfW∈-Lc1kon∩cLeknp ,t1r

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