By Nikolai K. Nikolski
Including the significant other quantity through an analogous writer, Operators, capabilities, and platforms: a simple studying. quantity 1: Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, Vol. ninety two, AMS, 2002, this certain paintings combines 4 significant themes of recent research and its functions: A. Hardy periods of holomorphic capabilities, B. Spectral conception of Hankel and Toeplitz operators, C. functionality types for linear operators and loose interpolations, and D. Infinite-dimensional procedure conception and sign processing. This quantity includes elements C and D. functionality versions for linear operators and unfastened interpolations: this can be a common subject and, certainly, is the main influential operator idea process within the post-spectral-theorem period. during this booklet, its ability is established by way of fixing generalized Carleson-type interpolation difficulties. Infinite-dimensional procedure concept and sign processing: This subject is the touchstone of the 3 formerly built thoughts. The presence of this utilized subject in a natural arithmetic surroundings displays vital adjustments within the mathematical panorama of the final two decades, in that the position of the most patron and patron of harmonic, complicated, and operator research has a growing number of handed from differential equations, scattering thought, and chance to regulate idea and sign processing. This and the significant other quantity are aimed toward a large viewers of readers, from graduate scholars to expert mathematicians. They boost an uncomplicated method of the topic whereas conserving knowledgeable point that may be utilized in complicated research and chosen functions.
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