MARC details
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05655nam a22004455i 4500 |
| 001 - CONTROL NUMBER |
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978-1-4419-7245-3 |
| 003 - CONTROL NUMBER IDENTIFIER |
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DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20180115171503.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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110217s2011 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781441972453 |
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978-1-4419-7245-3 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-1-4419-7245-3 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA276-280 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBT |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT029000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
519.5 |
| Edition number |
23 |
| 245 10 - TITLE STATEMENT |
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| Title |
Selected Works of Donald L. Burkholder |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
edited by Burgess Davis, Renming Song. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
1. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
New York, NY : |
| Name of producer, publisher, distributor, manufacturer |
Springer New York, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2011. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XXV, 729 p. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Selected Works in Probability and Statistics |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
On a class of stochastic approximation processes -- Sufficiency in the undominated case -- Iterates of conditional expectation operators -- On the order structure of the set of sufficient subfields -- Semi-Gaussian subspaces -- Successive conditional expectations of an integrable function -- Maximal inequalities as necessary conditions for almost everywhere convergence -- Martingale transforms. Ann. Math. Statist -- Extrapolation and interpolation of quasilinear operators on martingales -- A maximal function characterization of the class Hp -- Distribution function inequalities for the area integral -- Distribution function inequalities for martingales -- Boundary behaviour of harmonic functions in a half-space and Brownian motion -- One-sided maximal functions and Hp. J. Functional Analysis -- Boundary value estimation of the range of an analytic function -- A sharp inequality for martingale transforms -- Weak inequalities for exit times and analytic functions -- A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional -- Martingale transforms and the geometry of Banach spaces -- A nonlinear partial differential equation and the unconditional constant of the Haar system in Lp -- Boundary value problems and sharp inequalities for martingale transforms -- An elementary proof of an inequality of R. E. A. C. Paley -- Martingales and Fourier analysis in Banach spaces -- A sharp and strict Lp-inequality for stochastic integrals -- A proof of Pełczyn´ski’s conjecture for the Haar system -- Differential subordination of harmonic functions and martingales -- Explorations in martingale theory and its applications -- Strong differential subordination and stochastic integration -- The best constant in the Davis inequality for the expectation of the martingale square function -- Joseph L. Doob. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This book chronicles Donald Burkholder's thirty-five year study of martingales and its consequences. Here are some of the highlights. Pioneering work by Burkholder and Donald Austin on the discrete time martingale square function led to Burkholder and Richard Gundy's proof of inequalities comparing the quadratic variations and maximal functions of continuous martingales, inequalities which are now indispensable tools for stochastic analysis. Part of their proof showed how novel distributional inequalities between the maximal function and quadratic variation lead to inequalities for certain integrals of functions of these operators. The argument used in their proof applies widely and is now called the Burkholder-Gundy good lambda method. This uncomplicated and yet extremely elegant technique, which does not involve randomness, has become important in many parts of mathematics. The continuous martingale inequalities were then used by Burkholder, Gundy, and Silverstein to prove the converse of an old and celebrated theorem of Hardy and Littlewood. This paper transformed the theory of Hardy spaces of analytic functions in the unit disc and extended and completed classical results of Marcinkiewicz concerning norms of conjugate functions and Hilbert transforms. While some connections between probability and analytic and harmonic functions had previously been known, this single paper persuaded many analysts to learn probability. These papers together with Burkholder's study of martingale transforms led to major advances in Banach spaces. A simple geometric condition given by Burkholder was shown by Burkholder, Terry McConnell, and Jean Bourgain to characterize those Banach spaces for which the analog of the Hilbert transform retains important properties of the classical Hilbert transform. Techniques involved in Burkholder's usually successful pursuit of best constants in martingale inequalities have become central to extensive recent research into two well- known open problems, one involving the two dimensional Hilbert transform and its connection to quasiconformal mappings and the other a conjecture in the calculus of variations concerning rank-one convex and quasiconvex functions. This book includes reprints of many of Burkholder's papers, together with two commentaries on his work and its continuing impact. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Statistics. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Statistics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Statistical Theory and Methods. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Davis, Burgess. |
| Relator term |
editor. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Song, Renming. |
| Relator term |
editor. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9781441972446 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Selected Works in Probability and Statistics |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://dx.doi.org/10.1007/978-1-4419-7245-3">http://dx.doi.org/10.1007/978-1-4419-7245-3</a> |
| 912 ## - |
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ZDB-2-SMA |