Wave packet analysis of Feynman path integrals
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| Sprache: | English |
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Cham, Switzerland
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[2022]
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Volume 2305 |
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| 100 | 1 | |a Nicola, Fabio |0 (DE-588)1183842643 |4 aut | |
| 245 | 1 | 0 | |a Wave packet analysis of Feynman path integrals |c Fabio Nicola, S. Ivan Trapasso |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a xiii, 211 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v Volume 2305 | |
| 700 | 1 | |a Trapasso, S. Ivan |0 (DE-588)1265532559 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-0310-6186-8 |w (DE-604)BV048384388 |
| 830 | 0 | |a Lecture notes in mathematics |v Volume 2305 |w (DE-604)BV000676446 |9 2305 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-033825383 | ||
Datensatz im Suchindex
| _version_ | 1804184376471191552 |
|---|---|
| adam_text | Contents
Itinerary: How Gabor Analysis Met Feynman Path Integrals
1 1 The Elements of Gabor Analysts ccccccseaeeceeeeeaeereees
111 The Analysis of Functions via Gabor Wave Packets
1 2 The Analysis of Operators via Gabor Wave Packets 0 0005
121 The Problem of Quantization cccceseeeeeeeeeeeeees
122 Metaplectic Operators 00c cece cence eneeeeneneenenes
1 3 The Problem of Feynman Path Integrals 0:ccceaeeeeeeeens
131 Rigorous Time-Slicing Approximation of Feynman
Path Integrals 00 ccceeeseesc cnet seen eeeeeesenereeenenees
132 Pointwise Convergence at the Level of Integral
Kernels for Feynman-Trotter Parametrices : :0e000-
133 Convergence of Time-Slicing Approximations in
L(L?) for Low-Regular Potentials 00 ssecsseeeseueee
134 Convergence of Time-Slicing Approximations in the
| Ye
PartI Elements of Gabor Analysis
Basic Facts of Classical Analysis 0 0:scceeeeeeneeee rer eeennes
2 1 General Notation c cece cece cence ee tee teen eae teen eae eeaees
2 2 Function Spaces ccc cece e sees net e eee nae n eee eae eeeeneaseenees
221 Lebesgue Spaces cccce cece cece etn eeeeerensereenens
222 Differentiable Functions and Distributions
2 3 Basic Operations on Functions and Distributions 600065
2 4 The Fourier Transform 2uesesereenanennesn rer nennen sn e rennen
241 Convolution and Fourier Multipliers 2r0s seen
2 5 Some More Facıs and Notations surssneenersneennnnnnen nen
The Gabor Analysis of Functions - s-44sr4s20se sen en enn en nenn
3 1 Time-Frequency Representations :0eeeee cece eeeeneeetenees
311 The Short-Time Fourier Transform scceeseeseveeeee
312 Quadratic RepresentationS cccsseeeeeeseeeseeeeenn eee
3 2 Modulation Spaces cccssseereeeet reece net eseeees cere sees teres
3,3 Wiener Amalgam Spaces uesrmenseenensenenertenenessesenenn
34A Banach-Gelfand Triple of Modulation Spaces nennen
3 5 The Sjöstrand Class and Related Spaces cccceceeeeseneees
3 6 Complements een nennen
361 Weight Functions ue eenennenenenenennnenennnnteenen
362 The Cohen Class of Time-Frequency Representations
363 Kato-Sobolev Spaces +seseersereeeee nee renea rere eeees
364 Fourier Multipliers cecseseeseee sees esses eens ee eenes
365 More on the Sjdstrand Class : -s esses eee eee eens
366 Boundedness of Time-Frequency Transforms on
Modulation SpaceS +ecesee eee ee rene ee teense een eeeees
367 Gabor Frames ceee eee ee enero nent tae ne eens eae enens
4 The Gabor Analysis of Operators :ssccere reese cette eeeeeeees
4 1 The General Program scecse erect ee ee ere t nee ene ne neta ens
4 2 The Weyl Quantization cecereeee ee ee eter eee ne reenter ence es
4 3 Metaplectic Operators 000 0: cseeeeee ee eens nee ne tees eters teeta res
431 Notable Facts on Symplectic Matrices ceseeeeee eee
432 Metaplectic Operators: Definitions and Basic Properties
433 The Schrédinger Equation with Quadratic Hamiltonian
434 Symplectic Covariance of the Weyl Calculus
435 Gabor Matrix of Metaplectic Operators
4 4 Fourier and Oscillatory Integral Operators
442 Generalized Metaplectic Operators
4 5 Complements
451 Weyl Operators and Narrow Convergence
452 General Quantization Rules
453 The Class F10’(S, vs)
454 Finer Aspects of Gabor Wave Packet Analysis
5 Semiclassical Gabor Analysis
5 1 Semiclassical Transforms and Function Spaces
511 Sobolev Spaces and Embeddings
5 2 Semiclassical Quantization, Metaplectic Operators and FIOs
Part II Analysis of Feynman Path Integrals
6 Pointwise Convergence of the Integral Kernels
6 1 Summary
621 The Schwartz Kernel Theorem
622 Uniform Estimates for Linear
441 Canonical Transformations and the Associated Operators
443 Oscillatory Integral Operators with Rough Amplitude
Contents
Contents
xi
623 Exponentiation in Banach Algebras cceeceeeeeeeee 124
624 Two Technical Lemmas ccscceeseeesee eer enereencenees 125
6 3 Reduction to the Case A = (27 )T! ecco ccc ecccsccueceeeecaeeeeeens 126
6 4 The Fundamental Solution and the Trotter Formula - 127
6 5 Potentials in MGS neeeenseneeennnaneenenennenernennenennrennennnnnernen 132
6 6 Potentials in CE? cece c cee nee cece eee eeneeneneneeeneneereeea tenes 135
6 7 Potentials in the Sjéstrand Class M°! oo cccsccceeceeeeeneeeneees 136
6 8 Convergence at Exceptional Times e:cccsceeceeeeeeeeeeees 140
6 9 Physics at Exceptional Times 0 cccceeeeeeeeeneeeeeesenenes 143
7 Convergence in L(L?) for Potentials in the Sjéstrand Class 145
7 1 SUMMATY «0 cece eter e cree nee n rete nee nan eaeenanteee renee 145
7 2 An Abstract Approximation Result in £L(L?) u 148
7 3 Short-Time Analysis of the Action uessssssneearennenenernere 150
74 Estimates for the Parametrix and Convergence Results 154
8 Convergence in £(L7) for Potentials in Kato-Sobolev Spaces 161
8 1 Summary eeenenennsensensenensenensenesnenenneneenenesnnenesnenensen 161
8 2 Sobolev Regularity of the Hamiltonian Flow :escceseeees 163
8 3 Sobolev Regularity of the Classical Action serseerenenenee 172
8 4 Analysis of the Parametrices and Convergence Results - 174
8 5 Higher-Order Parametrices ccccccsaseeeeeneeee reese neeenees 178
9 Convergence in the L? Setting ccccccccc cence eee en ene eneenenes 183
QL SUMMATY 0 eee te eect ence nee ene nen e eens eet ener ee eee neta eee 183
9 2 Review of the Short Time Analysis in the Smooth Category 185
9 3 Wave Packet Analysis of the Schrödinger Flow -u -- 187
9 4 Convergence in L? with Loss of Derivatives :sssesesereeres 190
9 5 The Case of Magnetic Fields 1000 cece ec eeecee ee eneeeeseeeer erie 192
9 6 Sharpness of the Results c:cceceseneeeeeeeeeteeentenet arenes 195
9 7 Extensions to the Case of Rough Potentials - 0- seseeeee ees 197
Bibliography 0ccecc eee e cece eee eee een e eee en cree enone eran en eneaees 199
Unde x oo c cece cece eee e nee eee ene ee EEE SEE REED EEE EEE E EEE en Ee EER ES 209
|
| adam_txt |
Contents
Itinerary: How Gabor Analysis Met Feynman Path Integrals
1 1 The Elements of Gabor Analysts ccccccseaeeceeeeeaeereees
111 The Analysis of Functions via Gabor Wave Packets
1 2 The Analysis of Operators via Gabor Wave Packets 0 0005
121 The Problem of Quantization cccceseeeeeeeeeeeeees
122 Metaplectic Operators 00c cece cence eneeeeneneenenes
1 3 The Problem of Feynman Path Integrals 0:ccceaeeeeeeeens
131 Rigorous Time-Slicing Approximation of Feynman
Path Integrals 00 ccceeeseesc cnet seen eeeeeesenereeenenees
132 Pointwise Convergence at the Level of Integral
Kernels for Feynman-Trotter Parametrices : :0e000-
133 Convergence of Time-Slicing Approximations in
L(L?) for Low-Regular Potentials 00 ssecsseeeseueee
134 Convergence of Time-Slicing Approximations in the
| Ye
PartI Elements of Gabor Analysis
Basic Facts of Classical Analysis 0 0:scceeeeeeneeee rer eeennes
2 1 General Notation c cece cece cence ee tee teen eae teen eae eeaees
2 2 Function Spaces ccc cece e sees net e eee nae n eee eae eeeeneaseenees
221 Lebesgue Spaces cccce cece cece etn eeeeerensereenens
222 Differentiable Functions and Distributions
2 3 Basic Operations on Functions and Distributions 600065
2 4 The Fourier Transform 2uesesereenanennesn rer nennen sn e rennen
241 Convolution and Fourier Multipliers 2r0s seen
2 5 Some More Facıs and Notations surssneenersneennnnnnen nen
The Gabor Analysis of Functions - s-44sr4s20se sen en enn en nenn
3 1 Time-Frequency Representations :0eeeee cece eeeeneeetenees
311 The Short-Time Fourier Transform scceeseeseveeeee
312 Quadratic RepresentationS cccsseeeeeeseeeseeeeenn eee
3 2 Modulation Spaces cccssseereeeet reece net eseeees cere sees teres
3,3 Wiener Amalgam Spaces uesrmenseenensenenertenenessesenenn
34A Banach-Gelfand Triple of Modulation Spaces nennen
3 5 The Sjöstrand Class and Related Spaces cccceceeeeseneees
3 6 Complements een nennen
361 Weight Functions ue eenennenenenenennnenennnnteenen
362 The Cohen Class of Time-Frequency Representations
363 Kato-Sobolev Spaces +seseersereeeee nee renea rere eeees
364 Fourier Multipliers cecseseeseee sees esses eens ee eenes
365 More on the Sjdstrand Class : -s esses eee eee eens
366 Boundedness of Time-Frequency Transforms on
Modulation SpaceS +ecesee eee ee rene ee teense een eeeees
367 Gabor Frames ceee eee ee enero nent tae ne eens eae enens
4 The Gabor Analysis of Operators :ssccere reese cette eeeeeeees
4 1 The General Program scecse erect ee ee ere t nee ene ne neta ens
4 2 The Weyl Quantization cecereeee ee ee eter eee ne reenter ence es
4 3 Metaplectic Operators 000 0: cseeeeee ee eens nee ne tees eters teeta res
431 Notable Facts on Symplectic Matrices ceseeeeee eee
432 Metaplectic Operators: Definitions and Basic Properties
433 The Schrédinger Equation with Quadratic Hamiltonian
434 Symplectic Covariance of the Weyl Calculus
435 Gabor Matrix of Metaplectic Operators
4 4 Fourier and Oscillatory Integral Operators
442 Generalized Metaplectic Operators
4 5 Complements
451 Weyl Operators and Narrow Convergence
452 General Quantization Rules
453 The Class F10’(S, vs)
454 Finer Aspects of Gabor Wave Packet Analysis
5 Semiclassical Gabor Analysis
5 1 Semiclassical Transforms and Function Spaces
511 Sobolev Spaces and Embeddings
5 2 Semiclassical Quantization, Metaplectic Operators and FIOs
Part II Analysis of Feynman Path Integrals
6 Pointwise Convergence of the Integral Kernels
6 1 Summary
621 The Schwartz Kernel Theorem
622 Uniform Estimates for Linear
441 Canonical Transformations and the Associated Operators
443 Oscillatory Integral Operators with Rough Amplitude
Contents
Contents
xi
623 Exponentiation in Banach Algebras cceeceeeeeeeee 124
624 Two Technical Lemmas ccscceeseeesee eer enereencenees 125
6 3 Reduction to the Case A = (27 )T! ecco ccc ecccsccueceeeecaeeeeeens 126
6 4 The Fundamental Solution and the Trotter Formula - 127
6 5 Potentials in MGS neeeenseneeennnaneenenennenernennenennrennennnnnernen 132
6 6 Potentials in CE? cece c cee nee cece eee eeneeneneneeeneneereeea tenes 135
6 7 Potentials in the Sjéstrand Class M°! oo cccsccceeceeeeeneeeneees 136
6 8 Convergence at Exceptional Times e:cccsceeceeeeeeeeeeees 140
6 9 Physics at Exceptional Times 0 cccceeeeeeeeeneeeeeesenenes 143
7 Convergence in L(L?) for Potentials in the Sjéstrand Class 145
7 1 SUMMATY «0 cece eter e cree nee n rete nee nan eaeenanteee renee 145
7 2 An Abstract Approximation Result in £L(L?) u 148
7 3 Short-Time Analysis of the Action uessssssneearennenenernere 150
74 Estimates for the Parametrix and Convergence Results 154
8 Convergence in £(L7) for Potentials in Kato-Sobolev Spaces 161
8 1 Summary eeenenennsensensenensenensenesnenenneneenenesnnenesnenensen 161
8 2 Sobolev Regularity of the Hamiltonian Flow :escceseeees 163
8 3 Sobolev Regularity of the Classical Action serseerenenenee 172
8 4 Analysis of the Parametrices and Convergence Results - 174
8 5 Higher-Order Parametrices ccccccsaseeeeeneeee reese neeenees 178
9 Convergence in the L? Setting ccccccccc cence eee en ene eneenenes 183
QL SUMMATY 0 eee te eect ence nee ene nen e eens eet ener ee eee neta eee 183
9 2 Review of the Short Time Analysis in the Smooth Category 185
9 3 Wave Packet Analysis of the Schrödinger Flow -u -- 187
9 4 Convergence in L? with Loss of Derivatives :sssesesereeres 190
9 5 The Case of Magnetic Fields 1000 cece ec eeecee ee eneeeeseeeer erie 192
9 6 Sharpness of the Results c:cceceseneeeeeeeeeteeentenet arenes 195
9 7 Extensions to the Case of Rough Potentials - 0- seseeeee ees 197
Bibliography 0ccecc eee e cece eee eee een e eee en cree enone eran en eneaees 199
Unde x oo c cece cece eee e nee eee ene ee EEE SEE REED EEE EEE E EEE en Ee EER ES 209 |
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| author | Nicola, Fabio Trapasso, S. Ivan |
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| id | DE-604.BV048447164 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:29:35Z |
| indexdate | 2024-07-10T09:38:21Z |
| institution | BVB |
| isbn | 9783031061851 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033825383 |
| oclc_num | 1341225251 |
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| owner | DE-188 DE-83 DE-824 |
| owner_facet | DE-188 DE-83 DE-824 |
| physical | xiii, 211 Seiten Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Nicola, Fabio (DE-588)1183842643 aut Wave packet analysis of Feynman path integrals Fabio Nicola, S. Ivan Trapasso Cham, Switzerland Springer [2022] © 2022 xiii, 211 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2305 Trapasso, S. Ivan (DE-588)1265532559 aut Erscheint auch als Online-Ausgabe 978-3-0310-6186-8 (DE-604)BV048384388 Lecture notes in mathematics Volume 2305 (DE-604)BV000676446 2305 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033825383&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nicola, Fabio Trapasso, S. Ivan Wave packet analysis of Feynman path integrals Lecture notes in mathematics |
| title | Wave packet analysis of Feynman path integrals |
| title_auth | Wave packet analysis of Feynman path integrals |
| title_exact_search | Wave packet analysis of Feynman path integrals |
| title_exact_search_txtP | Wave packet analysis of Feynman path integrals |
| title_full | Wave packet analysis of Feynman path integrals Fabio Nicola, S. Ivan Trapasso |
| title_fullStr | Wave packet analysis of Feynman path integrals Fabio Nicola, S. Ivan Trapasso |
| title_full_unstemmed | Wave packet analysis of Feynman path integrals Fabio Nicola, S. Ivan Trapasso |
| title_short | Wave packet analysis of Feynman path integrals |
| title_sort | wave packet analysis of feynman path integrals |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033825383&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT nicolafabio wavepacketanalysisoffeynmanpathintegrals AT trapassosivan wavepacketanalysisoffeynmanpathintegrals |