Series: Springer Series in Statistics
2008, Approx. 500 p., Hardcover
ISBN: 978-0-387-75691-2
Due: March 2008
About this book
Collects the most important papers of Bradley Efron in one place
Adds comments by Efron and other important statisticians
A collection of journal articles by reknowned statistician Bradley Efron.
Table of contents
Foreword by Bradley Efron.-1. From 1965: The convex hull of a random set of points, Introduced by Tom Cover.- 2. From 1971: Forcing a sequential experiment to be balanced, Introduced by Herman Chernoff.-3. From 1975: Defining the curvature of a statistical problem (with applications to second order efficiency) Introduced by Rob Kass and Paul Vos.- 4. From 1975: Data analysis using Stein’s estimator and its generalizations (with Carl Morris), Introduced by John Rolph.- 5. From 1976: Estimating the number of unseen species: How many words did Shakespeare know? (with Ronald Thisted), Introduced by Peter McCullagh.- 6. From 1977: The efficiency of Cox’s likelihood function for censored data, Introduced by John Kalbfleisch.- 7. From 1977: Stein’s paradox in statistics (with Carl Morris), Introduced by Jim Berger.- 8. From 1978: Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information (with David V. Hinkley), Introduced by Thomas DiCiccio.- 9. From 1979: Bootstrap methods: Another look at the jackknife, Introduced by David Hinkley .- 10. From 1981: The jackknife estimate of variance (with Charles Stein), Introduced by Jun Shao and C.F. Jeff Wu.- 11. From 1982: The Jackknife, the Bootstrap and Other Resampling Plans [excerpt], Introduced by Peter Hall .- 12. From 1983: Estimating the error rate of a prediction rule: Improvement on cross-validation, Introduced by Trevor Hastie.- 13. From 1986: Why isn’t everyone a Bayesian?, Introduced by Larry Wasserman.- 14. From 1987: Better bootstrap confidence intervals,Introduced by Peter Bickel.- 15. From 1993: An Introduction to the Bootstrap (with Robert Tibshirani) [excerpt], Introduced by Rudy Beran.- 16. From 1996: Using specially designed exponential families for density estimation (with Robert Tibshirani), Introduced by Nancy Reid.- 17. From 1996: Bootstrap confidence levels for phylogenetic trees (correction) (with Elizabeth Halloran and Susan Holmes), Introduced by Joe Felsenstein.- 18. From 1998: R. A. Fisher in the 21st century, Introduced by Stephen Stigler.- 19. From 2001: Empirical Bayes analysis of a microarray experiment (with Robert Tibshirani, John D. Storey and Virginia Tusher), Introduced by Rafael Irizarry .- 20. From 2004: Least angle regression (with Trevor Hastie, Iain Johnstone and Robert Tibshirani), Introduced by David Madigan.- 21. From 2004: Large-scale simultaneous hypothesis testing: The choice of a null hypothesis, Introduced by Michael Newton.- President’s Corner by Bradley Efron (AMSTAT News, April 2004): “But What Do Statisticians Do?”.
Series: Pseudo-differential Operators , Vol. 1
2008, Approx. 350 p., Softcover
ISBN: 978-3-7643-8511-8
Due: May 2008
About this book
The book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators, spectral properties and complex powers of hypoelliptic operators, Schatten-von Neumann classes, the Connes-Wodzicki residue in Euclidean spaces, exponential decay of eigenfunctions, regularity and decay of homoclinics for semilinear equations and travelling waves.
The book is completely self-contained and accessible to graduate students.
Table of contents
Background Material.- Global Pseudo-differential Calculus.- Globally Hypoelliptic PDEs.- Spectral Properties of Pseudo-differential Operators.- Other Applications.- Appendix.- Bibliography.- Index.
Series: Operator Theory: Advances and Applications , Vol. 180
2008, Approx. 400 p., Hardcover
ISBN: 978-3-7643-8647-4
Due: May 2008
About this book
This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Applications are given to Maurey-Rosenthal factorization of operators and to classical operators arising in commutative harmonic analysis. The main tool is the vector measure associated to such an operator, which produces a corresponding space of integrable functions and an integration operator.
Table of contents
1. Introduction.- 2. Quasi-Banach Function Spaces.- 3. Vector Measures and Integration Operators.- 4. Optimal Domains and Integral Extensions.- 5. Operators which are p-th Power Factorable.- 6. Factorization of p-th Power Factorable Operators through Lp-Spaces.- 7. Operators from Classical Harmonic Analysis.
2007, 370 p., Hardcover
ISBN: 978-4-431-73239-6
About this book
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations -- from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as to many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas, providing interested researchers and students with valuable suggestions and instructive guidance for their work. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics. This dedication is made on the occasion of Professor Kawai's 60th birthday as a token of deep appreciation of the important contributions he has made to the field. Introductory notes on the scientific works of Professor Kawai are also included.
Table of contents
Part 1. The work of T. Kawai
Publications of Professor Takahiro Kawai
The work of T. Kawai on hyperfunction theory and microlocal analysis, Part 1 -- Microlocal analysis and differential equations by Nobuyuki Tose
The work of T. Kawai on hyperfunction theory and microlocal analysis, Part 2 -- Operators of infinite order and convolution equations by Takashi Aoki
The work of T. Kawai on exact WKB analysis by Yoshitsugu Takei
Part 2. Contributed papers
Virtual turning points -- A gift of microlocal analysis to the exact WKB analysis by Takashi Aoki, Naofumi Honda, Takahiro Kawai, Tatsuya Koike, Yukihiro Nishikawa, Shunsuke Sasaki, Akira Shudo, Yoshitsugu Takei
Regular sequences associated with the Noumi-Yamada equations with a large parameter by Takashi Aoki, Naofumi Honda
Ghost busting: Making sense of non-Hermitian Hamiltonians by Carl M. Bender
Vanishing of the logarithmic trace of generalized Szego projectors by Louis Boutet de Monvel
Nonlinear Stokes phenomena in first or second order differential equations by Ovidiu Costin
Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation by Yuki Daido, Hyeonbae Kang, Gen Nakamura
Exact WKB analysis near a simple turning point by Eric Delabaere
The Borel transform by Leon Ehrenpreis
On the use of Z-transforms in the summation of transseries for partial differential equations by Christopher J. Howls
Some dynamical aspects of Painleve VI by Katsunori Iwasaki
An algebraic representation for correlation functions in integrable spin chains by Michio Jimbo
Inverse image of D-modules and quasi-b-functions by Yves Laurent
The hypoelliptic Laplacian of J.-M. Bismut by Gilles Lebeau
Commuting differential operators with regular siongularities by Toshio Oshima
The behaviors of singular solutions of some partial differential equations in the complex domain by Sunao Ouchi
Observations on the JWKB treatment of the quadratic barrier by Hujun Shen, Harris J. Silverstone
A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Henon map by Akira Shudo
Spectral instability for non-selfadjoint operators by Johannes Sjostrand
Bondary and lens rigidity, tensor tomography and analytic microlocal analysis by Plamen Stefanov, Gunther Uhlmann
Coupling of two partial differential equations and its application by Hidetoshi Tahara
Instanton-type formal solutions for the first Painleve hierarchy by Yoshitsugu Takei
From exact-WKB toward singular quantum perturbation theory II by Andre Voros
WKB analysis and Poincare theorem for vector fields by Masafumi Yoshino