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The Resource Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems, by Damir Z. Arov, Harry Dym, (electronic resource)

Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems, by Damir Z. Arov, Harry Dym, (electronic resource)

Label
Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
Title
Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
Statement of responsibility
by Damir Z. Arov, Harry Dym
Creator
Contributor
Author
Subject
Language
eng
Summary
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.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Arov, Damir Z
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Dym, Harry
Series statement
  • Springer eBooks
  • Operator Theory: Advances and Applications,
  • Springer eBooks.
Series volume
266
http://library.link/vocab/subjectName
  • Mathematics
  • Operator theory
  • Probabilities
Label
Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems, by Damir Z. Arov, Harry Dym, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-70262-9
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- Analytic preliminaries -- The de Branges spaces B(E) and H(A) -- Three extension problems -- Spectral functions for ci problems -- Inverse spectral problems -- Generalizations -- Real and symmetric constraints -- Past and Future -- Conservative and passive systems -- Rational spectral densities
Control code
978-3-319-70262-9
Dimensions
unknown
Extent
1 online resource (XIV, 405 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319702629
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-70262-9
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1047680222
Label
Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems, by Damir Z. Arov, Harry Dym, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-70262-9
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- Analytic preliminaries -- The de Branges spaces B(E) and H(A) -- Three extension problems -- Spectral functions for ci problems -- Inverse spectral problems -- Generalizations -- Real and symmetric constraints -- Past and Future -- Conservative and passive systems -- Rational spectral densities
Control code
978-3-319-70262-9
Dimensions
unknown
Extent
1 online resource (XIV, 405 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319702629
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-70262-9
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1047680222

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