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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Hyponormal Quantization of Planar Domains - Exponential Transform in Dimension Two (Paperback, 1st ed. 2017)
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Hyponormal Quantization of Planar Domains - Exponential Transform in Dimension Two (Paperback, 1st ed. 2017)
Series: Lecture Notes in Mathematics, 2199
Expected to ship within 10 - 15 working days
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This book exploits the classification of a class of linear bounded
operators with rank-one self-commutators in terms of their spectral
parameter, known as the principal function. The resulting
dictionary between two dimensional planar shapes with a degree of
shade and Hilbert space operators turns out to be illuminating and
beneficial for both sides. An exponential transform, essentially a
Riesz potential at critical exponent, is at the heart of this novel
framework; its best rational approximants unveil a new class of
complex orthogonal polynomials whose asymptotic distribution of
zeros is thoroughly studied in the text. Connections with areas of
potential theory, approximation theory in the complex domain and
fluid mechanics are established. The text is addressed, with
specific aims, at experts and beginners in a wide range of areas of
current interest: potential theory, numerical linear algebra,
operator theory, inverse problems, image and signal processing,
approximation theory, mathematical physics.
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