Almost-orthogonality of restricted Haar functions
Copyright policy )Almost-orthogonality of restricted Haar functions
We consider the Haar functions h I h_I on dyadic intervals. We show that if p > 2 3 p>\frac 23 and E ⊂ [ 0 , 1 ] E\subset [0,1] , then the set of all functions ‖ h I 1 E ‖ 2 − 1 h I 1 E \|h_I1_E\|_2^{-1}h_I1_E with | I ∩ E | ≥ p | I | |I\cap E|\geq p|I| is a Riesz sequence. For p ≤ 2 3 p\leq \frac 23 we provide a counterexample.
- Aalto University Finland
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Mathematics - Functional Analysis, Haar functions, ta111, FOS: Mathematics, Riesz sequence, Functional Analysis (math.FA)
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Mathematics - Functional Analysis, Haar functions, ta111, FOS: Mathematics, Riesz sequence, Functional Analysis (math.FA)
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