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ON POINTWISE CONVERGENCE OF SCHRÖDINGER MEANS
Author(s) -
Dimou Evangelos,
Seeger Andreas
Publication year - 2020
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12025
Subject(s) - mathematics , pointwise convergence , pointwise , sobolev space , almost everywhere , convergence (economics) , characterization (materials science) , simple (philosophy) , regular polygon , space (punctuation) , combinatorics , real line , pure mathematics , mathematical analysis , geometry , physics , philosophy , linguistics , epistemology , optics , approx , computer science , economics , economic growth , operating system
For functions in the Sobolev space H s and decreasing sequencest n → 0 we examine convergence almost everywhere of the generalized Schrödinger means on the real line, given byS a f ( x , t n ) = exp ( i t n( − ∂ x x ) a / 2 ) f ( x ) ; here a > 0 , a ≠ 1 . For decreasing convex sequences we obtain a simple characterization of convergence a.e. for all functions in H s when 0 < s < min { a / 4 , 1 / 4 } and a ≠ 1 . We prove sharp quantitative local and global estimates for the associated maximal functions. We also obtain sharp results for the case a = 1 .