Haar Series and Linear Operators
11.2013β―Π³. Β· Mathematics and Its Applications ΠΠ½ΠΈΠ³Π° 367 Β· Springer Science & Business Media
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ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
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reportΠΡΠ΅Π½ΠΊΠΈΡΠ΅ ΠΈ ΠΎΡΠ·ΠΈΠ²ΠΈΡΠ΅ Π½Π΅ ΡΠ° ΠΏΠΎΡΠ²ΡΡΠ΄Π΅Π½ΠΈ Β ΠΠ°ΡΡΠ΅ΡΠ΅ ΠΏΠΎΠ²Π΅ΡΠ΅
ΠΡΠΈΡΠΊΠΎ Π·Π° ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
In 1909 Alfred Haar introduced into analysis a remarkable system which bears his name. The Haar system is a complete orthonormal system on [0,1] and the Fourier-Haar series for arbitrary continuous function converges uniformly to this function.
This volume is devoted to the investigation of the Haar system from the operator theory point of view. The main subjects treated are: classical results on unconditional convergence of the Haar series in modern presentation; Fourier-Haar coefficients; reproducibility; martingales; monotone bases in rearrangement invariant spaces; rearrangements and multipliers with respect to the Haar system; subspaces generated by subsequences of the Haar system; the criterion of equivalence of the Haar and Franklin systems.
Audience: This book will be of interest to graduate students and researchers whose work involves functional analysis and operator theory.
This volume is devoted to the investigation of the Haar system from the operator theory point of view. The main subjects treated are: classical results on unconditional convergence of the Haar series in modern presentation; Fourier-Haar coefficients; reproducibility; martingales; monotone bases in rearrangement invariant spaces; rearrangements and multipliers with respect to the Haar system; subspaces generated by subsequences of the Haar system; the criterion of equivalence of the Haar and Franklin systems.
Audience: This book will be of interest to graduate students and researchers whose work involves functional analysis and operator theory.
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