L2 -Uncertainty Principle for the Weinstein-Multiplier Operators

Abstract

The aim of this paper is establish the Heisenberg-Pauli-Weyl uncertainty principle and Donho-Stark's uncertainty principle for the Weinstein L 2 -multiplier operators.

Calderón's reproducing formulas for the poly-axially Lα2-multiplier operators

“…Proof: Let f ∈ L 2 α (IR n + ) and m ∈ L 1 α (IR n + ) L 2 α (IR n + ) satisfying (12). Assume that µ α (E) < ∞ and S 1 σ 2(2|α|+n) dΩ α (σ, x) < ∞.…”

“…Let f be a function in L 2 α (IR n + ) and m ∈ L 1 α L 2 α (IR n + )satisfying the admissibility condition(12). If f is ε-concentrated on E and T α,m,σ f is δ-concentrated on S, then m α,1 (µ α (E))…”

Uncertainty Principle for the Weinstein-Gabor Transforms

“…The lastest years, the uncertainty principles was investigate in many setting such as free metaplectic transformation [18], quadratic-phase Fourier transforms [15], linear canonical Fourier-Bessel wavelet transform [2], linear canonical Dunkl setting [11], and in Weinstein setting [12,13].…”