MARC details
| 000 -LEADER |
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04789cam a22003375a 4500 |
| 001 - CONTROL NUMBER |
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11300428 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20201128023613.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
121227s1981 nyu frb 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781461258650 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781461258674 (print) |
| 040 ## - CATALOGING SOURCE |
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| Modifying agency |
WaSeSS |
| -- |
EG-ScBUE |
| Language of cataloging |
eng |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515 |
| Edition number |
22 |
| Item number |
BAL |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Balakrishnan, A. V. |
| 9 (RLIN) |
38588 |
| 245 10 - TITLE STATEMENT |
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| Title |
Applied functional analysis / |
| Statement of responsibility, etc |
A. V. Balakrishnan. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
2nd ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
New York : |
| Name of publisher, distributor, etc |
Springer-Verlag, |
| Date of publication, distribution, etc |
1981. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xiii, 373 p. ; |
| Accompanying material |
24 cm. |
| 490 0# - Series Statement |
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| Series statement |
Applications of mathematics ; |
| Volume/sequential designation |
3 |
| 500 ## - GENERAL NOTE |
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| General note |
Index : p. 370-373. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Bibliography : p. 367-369. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1 Basic Properties of Hilbert Spaces -- 1.0 Introduction -- 1.1 Basic Definitions -- 1.2 Examples of Hilbert Spaces -- 1.3 Hilbert Spaces from Hilbert Spaces -- 1.4 Convex Sets and Projections -- 1.5 Orthogonality and Orthonormal Bases -- 1.6 Continuous Linear Functionals -- 1.7 Riesz Representation Theorem -- 1.8 Weak Convergence -- 1.9 Nonlinear Functionals and Generalized Curves -- 1.10 The Hahn-Banach Theorem -- 2 Convex Sets and Convex Programming -- 2.0 Introduction -- 2.1 Elementary Notions -- 2.2 Support Functional of a Convex Set -- 2.3 Minkowski Functional -- 2.4 The Support Mapping -- 2.5 Separation Theorem -- 2.6 Application to Convex Programming -- 2.7 Generalization to Infinite Dimensional Inequalities -- 2.8 A Fundamental Result of Game Theory: Minimax Theorem -- 2.9 Application: Theorem of Farkas -- 3 Functions, Transformations, Operators -- 3.0 Introduction -- 3.1 Linear Operators and their Adjoints -- 3.2 Spectral Theory of Operators -- 3.3 Spectral Theory of Compact Operators -- 3.4 Operators on Separable Hilbert Spaces -- 3.5 L2 Spaces over Hilbert Spaces -- 3.6 Multilinear Forms -- 3.7 Nonlinear Volterra Operators -- 4 Semigroups of Linear Operators -- 4.0 Introduction -- 4.1 Definitions and General Properties of Semigroups -- 4.2 Generation of Semigroups -- 4.3 Semigroups over Hilbert Spaces: Dissipative Semigroups -- 4.4 Compact Semigroups -- 4.5 Analytic (Holomorphic) Semigroups -- 4.6 Elementary Examples of Semigroups -- 4.7 Extensions -- 4.8 Differential Equations: Cauchy Problem -- 4.9 Controllability -- 4.10 State Reduction: Observability -- 4.11 Stability and Stabilizability -- 4.12 Boundary Input: An Example -- 4.13 Evolution Equations -- 5 Optimal Control Theory -- 5.0 Introduction -- 5.1 Preliminaries -- 5.2 Linear Quadratic Regulator Problem -- 5.3 Linear Quadratic Regulator Problem: Infinite Time Interval -- 5.4 Hard Constraints -- 5.5 Final Value Control -- 5.6 Time Optimal Control Problem -- 6 Stochastic Optimization Theory -- 6.0 Introduction -- 6.1 Preliminaries -- 6.2 Measures on Cylinder Sets -- 6.3 Characteristic Functions and Countable Additivity -- 6.4 Weak Random Variables -- 6.5 Random Variables -- 6.6 White Noise -- 6.7 Differential Systems -- 6.8 The Filtering Problem -- 6.9 Stochastic Control -- 6.10 Physical Random Variables -- 6.11 Radon-Nikodym Derivatives -- 6.12 Nonlinear Stochastic Equations. |
| 506 ## - RESTRICTIONS ON ACCESS NOTE |
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| Terms governing access |
License restrictions may limit access. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
In preparing the second edition, I have taken advantage of the opportunity to correct errors as well as revise the presentation in many places. New material has been included, in addition, reflecting relevant recent work. The help of many colleagues (and especially Professor J. Stoer) in ferreting out errors is gratefully acknowledged. I also owe special thanks to Professor v. Sazonov for many discussions on the white noise theory in Chapter 6. February, 1981 A. V. BALAKRISHNAN v Preface to the First Edition The title "Applied Functional Analysis" is intended to be short for "Functional analysis in a Hilbert space and certain of its applications," the applications being drawn mostly from areas variously referred to as system optimization or control systems or systems analysis. One of the signs of the times is a discernible tilt toward application in mathematics and conversely a greater level of mathematical sophistication in the application areas such as economics or system science, both spurred undoubtedly by the heightening pace of digital computer usage. This book is an entry into this twilight zone. The aspects of functional analysis treated here are rapidly becoming essential in the training at the advance graduate level of system scientists and/or mathematical economists. There are of course now available many excellent treatises on functional analysis. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| Source of heading or term |
BUEsh |
| 9 (RLIN) |
2018 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Global analysis (Mathematics) |
| Source of heading or term |
BUEsh |
| 9 (RLIN) |
12358 |
| 653 ## - INDEX TERM--UNCONTROLLED |
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| Resource For college |
Engineering, Electrical |
| Arrived date list |
October2015 |
| 655 ## - INDEX TERM--GENRE/FORM |
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| Form subdivision |
Reading book |
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34232 |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 910 ## - USER-OPTION DATA (OCLC) |
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| User-option data |
Vendor-generated brief record |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| 952 ## - LOCATION AND ITEM INFORMATION (KOHA) |
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| -- |
2015-10-27 |