The $(abc,pqr)$-problem for Approximate Schauder Frames for Banach Spaces

Abstract

Motivated from the complete solution of important $abc$-problem for Gabor system for the Hilbert space ${\mathcal{L}}^2(\mathbb{R})$ by Dai and Sun [\textit{Memoirs of Amer. Math. Soc., 2016}] and from the existential result of approximate Schauder frames for ${\mathcal{L}}^p(\mathbb{R})$ using translation operators on ${\mathcal{L}}^p(\mathbb{R})$ by Freeman, Odell, Schlumprecht, and Zsak [\textit{Israel. J. Math, 2014}], we formulate $(abc,pqr)$-problem for approximate Schauder frames for Banach spaces ${\mathcal{L}}^p(\mathbb{R})$, $1<p<\infty$.

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