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On the frame properties of exponentials associated to analytic families of operators and application

  • S. Charfi and H. Ellouz
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Operator Theory
This chapter is in the book Operator Theory

Abstract

In the present paper, we are mainly concerned with the existence of frames of exponential families associated to the operator (I + εK)−1 d4 / dx4 + ε(I + εK)−1K( d4 / dx4 − ( d4 / dx4 ) 12 ) in L2(−T, T), T > 0, where K is the integral operator with kernel being the Hankel function of the first kind and order 0. Via a specific growth inequality, we extend this problem to a theoretical one and study the existence of frame of exponentials.

Abstract

In the present paper, we are mainly concerned with the existence of frames of exponential families associated to the operator (I + εK)−1 d4 / dx4 + ε(I + εK)−1K( d4 / dx4 − ( d4 / dx4 ) 12 ) in L2(−T, T), T > 0, where K is the integral operator with kernel being the Hankel function of the first kind and order 0. Via a specific growth inequality, we extend this problem to a theoretical one and study the existence of frame of exponentials.

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