Holdings: Mathematical scattering theory :: Universität Regensburg

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Bibliographic Details
Title:	Mathematical scattering theory analytical theory
From:	D. R. Yafaev
Person:	Jafaev, Dmitrij R. 1948-2024 Verfasser aut
Main Author:	Jafaev, Dmitrij R. 1948-2024 (Author)
Format:	Book
Language:	English
Published:	Providence, RI American Math. Soc. 2010
Series:	Mathematical surveys and monographs 158
Notation:	SK 620
Subjects:	Störungstheorie
Online Access:	http://www.gbv.de/dms/tib-ub-hannover/605125562.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020682668&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XIII, 444 S.
ISBN:	9780821803318

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MARC


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Record in the Search Index

DE-BY-UBR_call_number	8011/SK 620 Y12 803/SK 620 Y12
DE-BY-UBR_katkey	4708834
DE-BY-UBR_location	UB Handapparat Mathematik Prof. Finster-Zirker UB Handapparat Mathematik Prof. Ammann
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adam_text	IMAGE 1 MATHEMATICAL SCATTERING THEORY ANALYTIC THEORY D. R.YAFAEV AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND IMAGE 2 CONTENTS PREFACE XI BASIC NOTATION 1 INTRODUCTION 5 CHAPTER 0. BASIC CONCEPTS 17 1. CLASSIFICATION OF THE SPECTRUM 17 2. CLASSES OF COMPACT OPERATORS 20 3. THE RESOLVENT EQUATION. CONDITIONS FOR SELF-ADJOINTNESS 23 4. WAVE OPERATORS (WO) 26 5. THE SMOOTH METHOD 29 6. THE STATIONARY SCHEME 33 7. THE SCATTERING OPERATOR AND THE SCATTERING MATRIX (SM) 38 8. THE TRACE CLASS METHOD 42 9. THE SPECTRAL SHIFT FUNCTION (SSF) AND THE PERTURBATION DETERMINANT (PD) 45 10. DIFFERENTIAL OPERATORS 52 11. FUNCTION SPACES AND EMBEDDING THEOREMS 56 12. PSEUDODIFFERENTIAL OPERATORS 58 13. MISCELLANEOUS ANALYTIC FACTS 67 CHAPTER 1. SMOOTH THEORY. THE SCHRODINGER OPERATOR 71 1. TRACE THEOREMS 71 2. THE FREE HAMILTONIAN 75 3. THE SCHRODINGER OPERATOR 79 4. EXISTENCE OF WAVE OPERATORS 82 5. WAVE OPERATORS FOR LONG-RANGE POTENTIALS 86 6. COMPLETENESS OF WAVE OPERATORS 93 7. THE LIMITING ABSORPTION PRINCIPLE (LAP) 95 8. THE SCATTERING MATRIX 96 9. ABSENCE OF THE SINGULAR CONTINUOUS SPECTRUM 98 10. GENERAL DIFFERENTIAL OPERATORS OF SECOND ORDER 101 11. THE PERTURBED POLYHARMONIC OPERATOR 103 12. THE PAULI AND DIRAC OPERATORS 104 CHAPTER 2. SMOOTH THEORY. GENERAL DIFFERENTIAL OPERATORS 109 1. SPECTRAL ANALYSIS OF DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTS 109 2. SCALAR DIFFERENTIAL OPERATORS 116 3. NONELLIPTIC DIFFERENTIAL OPERATORS 118 4. MATRIX DIFFERENTIAL OPERATORS 122 VII IMAGE 3 VIII CONTENTS 5. SCATTERING PROBLEMS FOR PERTURBATIONS OF A MEDIUM 124 6. STRONGLY PROPAGATIVE SYSTEMS. MAXWELL'S EQUATIONS 128 CHAPTER 3. SCATTERING FOR PERTURBATIONS OF TRACE CLASS TYPE 133 1. CONDITIONS ON AN INTEGRAL OPERATOR TO BE TRACE CLASS 133 2. PERTURBATIONS OF DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTS 136 3. THE SCHRODINGER OPERATOR 139 4. THE PERTURBED POLYHARMONIC OPERATOR 145 5. GENERAL DIFFERENTIAL OPERATORS OF SECOND ORDER 147 6. SCATTERING PROBLEMS FOR PERTURBATIONS OF A MEDIUM 154 7. WAVE EQUATION 157 8. THE SCATTERING MATRIX AND THE SPECTRAL SHIFT FUNCTION 159 CHAPTER 4. SCATTERING ON THE HALF-LINE 161 1. JOST SOLUTIONS. VOLTERRA EQUATIONS 161 2. GENERALIZED FOURIER TRANSFORM AND WO 170 3. LOW-ENERGY ASYMPTOTICS 178 4. HIGH-ENERGY ASYMPTOTICS 188 5. THE SSF FOR THE RADIAL SCHRODINGER OPERATOR 191 6. TRACE IDENTITIES 198 7. PERTURBATION BY A BOUNDARY CONDITION. POINT INTERACTION 203 CHAPTER 5. ONE-DIMENSIONAL SCATTERING 209 1. A DIRECT APPROACH 209 2. LOW- AND HIGH-ENERGY ASYMPTOTICS 216 3. THE SSF AND TRACE IDENTITIES 221 4. POTENTIALS WITH DIFFERENT LIMITS AT " + " AND " - " INFINITIES 223 CHAPTER 6. THE LIMITING ABSORPTION PRINCIPLE (LAP), THE RADIATION CONDITIONS AND THE EXPANSION THEOREM 231 1. ABSENCE OF POSITIVE EIGENVALUES AND RADIATION CONDITIONS 231 2. BOUNDARY VALUES OF THE RESOLVENT 233 3. A SHARP FORM OF THE LIMITING ABSORPTION PRINCIPLE 235 4. NONHOMOGENEOUS SCHRODINGER EQUATION 239 5. HOMOGENEOUS SCHRODINGER EQUATION 241 6. EXPANSION THEOREM 245 7. THE WAVE FUNCTION. THE SCATTERING AMPLITUDE 251 8. A GENERALIZED FOURIER INTEGRAL 255 9. THE MOURRE METHOD 259 CHAPTER 7. HIGH- AND LOW-ENERGY ASYMPTOTICS 267 1. HIGH-ENERGY AND UNIFORM RESOLVENT ESTIMATES 267 2. ASYMPTOTIC EXPANSION OF THE GREEN FUNCTION FOR LARGE VALUES OF THE SPECTRAL PARAMETER 275 3. SMALL TIME ASYMPTOTICS OF THE HEAT KERNEL 280 4. LOW-ENERGY BEHAVIOR OF THE RESOLVENT 285 5. LOW-ENERGY BEHAVIOR OF THE RESOLVENT. SLOWLY DECREASING POTENTIALS 291 CHAPTER 8. THE SCATTERING MATRIX (SM) AND THE SCATTERING CROSS SECTION 297 1. BASIC PROPERTIES OF THE SM 297 IMAGE 4 CONTENTS IX 2. THE SPECTRUM OF THE SM. THE MODIFIED SM 302 3. THE SCATTERING CROSS SECTION 306 4. HIGH-ENERGY ASYMPTOTICS OF THE SM. THE RAY EXPANSION 311 5. THE EIKONAL APPROXIMATION 319 6. THE AVERAGED SCATTERING CROSS SECTION. SINGULAR POTENTIALS 328 7. THE SEMICLASSICAL LIMIT 337 CHAPTER 9. THE SPECTRAL SHIFT FUNCTION AND TRACE FORMULAS 341 1. THE REGULARIZED PD AND SSF FOR THE MULTIDIMENSIONAL SCHRODINGER OPERATOR 341 2. HIGH-ENERGY ASYMPTOTICS OF THE SSF 353 3. TRACE IDENTITIES FOR THE MULTIDIMENSIONAL SCHRODINGER OPERATOR 365 CHAPTER 10. THE SCHRODINGER OPERATOR WITH A LONG-RANGE POTENTIAL 369 1. PROPAGATION ESTIMATES 369 2. LONG-RANGE SCATTERING 374 3. THE EIKONAL AND TRANSPORT EQUATIONS 380 4. SCATTERING MATRIX FOR LONG-RANGE POTENTIALS 384 CHAPTER 11. THE LAP AND RADIATION ESTIMATES REVISITED 399 1. THE EFFICIENT FORM OF THE LAP 399 2. ABSENCE OF POSITIVE EIGENVALUES AND UNIQUENESS THEOREM 403 3. NONHOMOGENEOUS SCHRODINGER EQUATION WITH A LONG-RANGE POTENTIAL 408 REVIEW OF THE LITERATURE 415 BIBLIOGRAPHY 429 INDEX 441
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author	Jafaev, Dmitrij R. 1948-2024
author_GND	(DE-588)122077431
author_facet	Jafaev, Dmitrij R. 1948-2024
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dewey-ones	515 - Analysis
dewey-raw	515.724
dewey-search	515.724
dewey-sort	3515.724
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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isbn	9780821803318
language	English
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physical	XIII, 444 S.
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spellingShingle	Jafaev, Dmitrij R. 1948-2024 Mathematical scattering theory analytical theory Mathematical surveys and monographs Störungstheorie (DE-588)4128420-3 gnd
subject_GND	(DE-588)4128420-3
title	Mathematical scattering theory analytical theory
title_auth	Mathematical scattering theory analytical theory
title_exact_search	Mathematical scattering theory analytical theory
title_full	Mathematical scattering theory analytical theory D. R. Yafaev
title_fullStr	Mathematical scattering theory analytical theory D. R. Yafaev
title_full_unstemmed	Mathematical scattering theory analytical theory D. R. Yafaev
title_short	Mathematical scattering theory
title_sort	mathematical scattering theory analytical theory
title_sub	analytical theory
topic	Störungstheorie (DE-588)4128420-3 gnd
topic_facet	Störungstheorie
url	http://www.gbv.de/dms/tib-ub-hannover/605125562.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020682668&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000018014
work_keys_str_mv	AT jafaevdmitrijr mathematicalscatteringtheoryanalyticaltheory

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