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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems (Paperback, Softcover reprint of the original 1st ed. 2018)
Loot Price: R3,481
Discovery Miles 34 810
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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems (Paperback, Softcover reprint of the original 1st ed. 2018)
Series: Operator Theory: Advances and Applications, 266
Expected to ship within 10 - 15 working days
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This monograph deals primarily with the prediction of vector valued
stochastic processes that are either weakly stationary, or have
weakly stationary increments, from finite segments of their past.
The main focus is on the analytic counterpart of these problems,
which amounts to computing projections onto subspaces of a Hilbert
space of p x 1 vector valued functions with an inner product that
is defined in terms of the p x p matrix valued spectral density of
the process. The strategy is to identify these subspaces as vector
valued de Branges spaces and then to express projections in terms
of the reproducing kernels of these spaces and/or in terms of a
generalized Fourier transform that is obtained from the solution of
an associated inverse spectral problem. Subsequently, the
projection of the past onto the future and the future onto the past
is interpreted in terms of the range of appropriately defined
Hankel operators and their adjoints, and, in the last chapter,
assorted computations are carried out for rational spectral
densities. The underlying mathematics needed to tackle this class
of problems is developed in careful detail, but, to ease the
reading, an attempt is made to avoid excessive generality. En route
a number of results that, to the best of our knowledge, were only
known for p = 1 are generalized to the case p > 1.
General
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