Convolution-like structures, differential operators and diffusion processes:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2022]
|
| Schriftenreihe: | Lecture notes in mathematics
Volume 2315 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 259 Seiten Illustrationen |
| ISBN: | 9783031052958 9783031052972 |
Internformat
MARC
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| 100 | 1 | |a Sousa, Rúben |0 (DE-588)1265686998 |4 aut | |
| 245 | 1 | 0 | |a Convolution-like structures, differential operators and diffusion processes |c Rúben Sousa, Manuel Guerra, Semyon Yakubovich |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a xii, 259 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v Volume 2315 | |
| 700 | 1 | |a Guerra, Manuel |0 (DE-588)1251247164 |4 aut | |
| 700 | 1 | |a Yakubovich, Semyon |0 (DE-588)1266615245 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-05296-5 |
| 830 | 0 | |a Lecture notes in mathematics |v Volume 2315 |w (DE-604)BV000676446 |9 2315 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 Introduction s2sssseensenensnenennnanennsenssennsnennnnnsnerennn 1
1 1 Motivation and Scope cece cece eee e nee e eee eee eee neseneneeeeee 1
1 2 Organization of the Book eccnaeseueneneanensnnenennennansnnansen 5
2 Preliminaries scssscssessnennenenensnnnnensenenennneenennrnenensen 9
2 1 Continuous-Time Markov Processes ccescceeeeeeeeeeneteneeeee 9
2 2 Sturm-Liouville Theory 0000 ccccccee cece ees eceena eens ens eneeenes 17
221 Solutions of the Sturm-Liouville Equation 665 18
222 Eigenfunction Expamsions c cseeceee sete eeceeee ees 22
223 Diffusion Semigroups Generated by Sturm-Liouville
Operators 1 0 cece ee terrence e ee en eer n anes renee eens 28
224 Remarkable Particular Cases 0 0ceeseeee ee eeeeeeee ences 30
2 3 Generalized Convolutions and Hypergroups ceceeeeeeeees 35
2 4 Harmonic Analysis with Respect to the Kingman Convolution 43
3 The Whittaker Convolution seseesneseseseeneneneesenennnnen 51
31A Special Case: The Kontorovich-Lebedev Convolution - 52
3 2 The Product Formula for the Whittaker Function 5665 53
3 3 Whittaker Translation : csccessceeeece ee eceeeee eee eeeneeeeaeees 64
3 4 Index Whittaker Transforms cceceesesee eee eee teeter eee en enes 71
3 5 Whittaker Convolution of Measures ceneensenssensenenerannnn nenn 80
351 Infinitely Divisible Distributions ernennen 82
352 Levy-Khintchine Type Representation uneeeeesennen 85
3 6 Lévy Processes with Respect to the Whittaker Convolution 89
361 Convolution Semigroups : ceeseee eens tree ene ee ene es 89
362 Lévy and Gaussian Processes s cssceserecsen ese eee eves 93
363 Some Auxiliary Results on the Whittaker Translation 98
364 Moment Functions neessereenensenenpennenenenenssneno nenn 101
365 Le amp;vy-Type Characterization of the Shiryaev Process 108
3 7 Whittaker Convolution of Functions 0ceseeee ease etree enna en 111
371 Mapping Properties in the Spaces LP (ra) cccvncneeneeeeeneenen 112
vii
viii
Contents
372 The Convolution Banach Algebra Zaun - 222220 een 116
3 8 Convolution-Type Integral Equations ee eeseseeceeeeas 120
Generalized Convolutions for Sturm-Liouville Operators , 127
4 1 Known Results and Motivation see bees ev ee eect eneseteeeeeeenenernres 2
4 2 Laplace-Type Representation perteteeecttetereeneteeeeeeeeeeeees
43 The Existence Theorem for Sturm-Liouville Product Formulas 139
43,1 The Associated Hyperbolic Cauchy Problem 139
432 The Time-Shifted Product Formula nn 145
433 The Product Formula for w as the Limit Case 147
4 4 Sturm-Liouville Transform of Measures cc nn 150
4 5 Sturm-Liouville Convolution of Measures nn 153
451 Infinite Divisibility and Levy-Khintchine Type
Represenation nenannenennneennnnnnnnnnnnennnnnnnnnnnnnnnnn 156
45 2 Convolution Semigroups 00 0 ee csceeeeccaeesccccueecess 158
45 3 Additive and Lévy Processes eeeccecssesecceccc 159
4 6 Sturm-Liouville HYPergroups 000 ceeeccceceeecesecesecersceece 165
46 1 The Nondegenerate Case u uu2u 222200 en 165
462 The Degenerate Case: Degenerate Hypergroups of
Full Support ec ceeeseeeicsceceeeeecccecc 171
4 7 Harmonic Analysis on L? Se 175
qr AFamily of L! Spaces 176
47 2 Application to Convolution-Type Integral Equations 180
Sonvolution-Like Structures on Multidimensional Spaces 183
some ons Associated with Conservative Strong Feller
OOPS 183
5 2 Nonexistenes of Convolutign cn reg tite iteeceees
on Bounded Domains os * DRsion Processes 196
521 Special Cases and Numerical Examples 197
523 poe Aunilary Results een 201
2 3 Eigenfunction Expansions, Critical Points
‚and Nonexistence Theorems 203
5 3 Nonexi Stence Of Convolutions en eter tt itteceeeeeeeaeacees
5 4 Families of C Ons: One-Dimensional Diffusions 207
OI Convolutions on Rieman Ss
with Cone-Like Metrics man Structures 14
rn 2
The Eigenfunction Expansion of the
Laplace-Betır
5 42 ami Operator 216
+2 Product Formulas and Convolgag oe
543 Infinitely Divisible M, UNS nn 224
Semigroups “*sures and Convolution
saa Special Cases es enessessenensennneseeee 35
Product Formulas and 000000 Tennessee 23
with Elliptic 9 a and Convolutions Associated
Perators on Subsets of R?
Contents ix
A Some Open Problems 2u-2224ssesseennenensnenenennenersnn nenne 247
References 2 c cece een e ene ene ene eee eae eee been ene teen enna teen ee ge 249
|
| adam_txt |
Contents
1 Introduction s2sssseensenensnenennnanennsenssennsnennnnnsnerennn 1
1 1 Motivation and Scope cece cece eee e nee e eee eee eee neseneneeeeee 1
1 2 Organization of the Book eccnaeseueneneanensnnenennennansnnansen 5
2 Preliminaries scssscssessnennenenensnnnnensenenennneenennrnenensen 9
2 1 Continuous-Time Markov Processes ccescceeeeeeeeeeneteneeeee 9
2 2 Sturm-Liouville Theory 0000 ccccccee cece ees eceena eens ens eneeenes 17
221 Solutions of the Sturm-Liouville Equation 665 18
222 Eigenfunction Expamsions c cseeceee sete eeceeee ees 22
223 Diffusion Semigroups Generated by Sturm-Liouville
Operators 1 0 cece ee terrence e ee en eer n anes renee eens 28
224 Remarkable Particular Cases 0 0ceeseeee ee eeeeeeee ences 30
2 3 Generalized Convolutions and Hypergroups ceceeeeeeeees 35
2 4 Harmonic Analysis with Respect to the Kingman Convolution 43
3 The Whittaker Convolution seseesneseseseeneneneesenennnnen 51
31A Special Case: The Kontorovich-Lebedev Convolution - 52
3 2 The Product Formula for the Whittaker Function 5665 53
3 3 Whittaker Translation : csccessceeeece ee eceeeee eee eeeneeeeaeees 64
3 4 Index Whittaker Transforms cceceesesee eee eee teeter eee en enes 71
3 5 Whittaker Convolution of Measures ceneensenssensenenerannnn nenn 80
351 Infinitely Divisible Distributions ernennen 82
352 Levy-Khintchine Type Representation uneeeeesennen 85
3 6 Lévy Processes with Respect to the Whittaker Convolution 89
361 Convolution Semigroups : ceeseee eens tree ene ee ene es 89
362 Lévy and Gaussian Processes s cssceserecsen ese eee eves 93
363 Some Auxiliary Results on the Whittaker Translation 98
364 Moment Functions neessereenensenenpennenenenenssneno nenn 101
365 Le amp;vy-Type Characterization of the Shiryaev Process 108
3 7 Whittaker Convolution of Functions 0ceseeee ease etree enna en 111
371 Mapping Properties in the Spaces LP (ra) cccvncneeneeeeeneenen 112
vii
viii
Contents
372 The Convolution Banach Algebra Zaun - 222220 een 116
3 8 Convolution-Type Integral Equations ee eeseseeceeeeas 120
Generalized Convolutions for Sturm-Liouville Operators , 127
4 1 Known Results and Motivation see bees ev ee eect eneseteeeeeeenenernres 2
4 2 Laplace-Type Representation perteteeecttetereeneteeeeeeeeeeeees
43 The Existence Theorem for Sturm-Liouville Product Formulas 139
43,1 The Associated Hyperbolic Cauchy Problem 139
432 The Time-Shifted Product Formula nn 145
433 The Product Formula for w as the Limit Case 147
4 4 Sturm-Liouville Transform of Measures cc nn 150
4 5 Sturm-Liouville Convolution of Measures nn 153
451 Infinite Divisibility and Levy-Khintchine Type
Represenation nenannenennneennnnnnnnnnnnennnnnnnnnnnnnnnnn 156
45 2 Convolution Semigroups 00 0 ee csceeeeccaeesccccueecess 158
45 3 Additive and Lévy Processes eeeccecssesecceccc 159
4 6 Sturm-Liouville HYPergroups 000 ceeeccceceeecesecesecersceece 165
46 1 The Nondegenerate Case u uu2u 222200 en 165
462 The Degenerate Case: Degenerate Hypergroups of
Full Support ec ceeeseeeicsceceeeeecccecc 171
4 7 Harmonic Analysis on L? Se 175
qr AFamily of L! Spaces 176
47 2 Application to Convolution-Type Integral Equations 180
Sonvolution-Like Structures on Multidimensional Spaces 183
some ons Associated with Conservative Strong Feller
OOPS 183
5 2 Nonexistenes of Convolutign cn reg tite iteeceees
on Bounded Domains os * DRsion Processes 196
521 Special Cases and Numerical Examples 197
523 poe Aunilary Results een 201
2 3 Eigenfunction Expansions, Critical Points
‚and Nonexistence Theorems 203
5 3 Nonexi Stence Of Convolutions en eter tt itteceeeeeeeaeacees
5 4 Families of C Ons: One-Dimensional Diffusions 207
OI Convolutions on Rieman Ss
with Cone-Like Metrics man Structures 14
rn 2
The Eigenfunction Expansion of the
Laplace-Betır
5 42 ami Operator 216
+2 Product Formulas and Convolgag oe
543 Infinitely Divisible M, UNS nn 224
Semigroups “*sures and Convolution
saa Special Cases es enessessenensennneseeee 35
Product Formulas and 000000 Tennessee 23
with Elliptic 9 a and Convolutions Associated
Perators on Subsets of R?
Contents ix
A Some Open Problems 2u-2224ssesseennenensnenenennenersnn nenne 247
References 2 c cece een e ene ene ene eee eae eee been ene teen enna teen ee ge 249 |
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| id | DE-604.BV048447039 |
| illustrated | Illustrated |
| index_date | 2024-07-03T20:29:33Z |
| indexdate | 2024-07-10T09:38:21Z |
| institution | BVB |
| isbn | 9783031052958 9783031052972 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033825260 |
| oclc_num | 1341392436 |
| open_access_boolean | |
| owner | DE-188 DE-83 DE-824 |
| owner_facet | DE-188 DE-83 DE-824 |
| physical | xii, 259 Seiten Illustrationen |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Sousa, Rúben (DE-588)1265686998 aut Convolution-like structures, differential operators and diffusion processes Rúben Sousa, Manuel Guerra, Semyon Yakubovich Cham, Switzerland Springer [2022] © 2022 xii, 259 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2315 Guerra, Manuel (DE-588)1251247164 aut Yakubovich, Semyon (DE-588)1266615245 aut Erscheint auch als Online-Ausgabe 978-3-031-05296-5 Lecture notes in mathematics Volume 2315 (DE-604)BV000676446 2315 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033825260&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sousa, Rúben Guerra, Manuel Yakubovich, Semyon Convolution-like structures, differential operators and diffusion processes Lecture notes in mathematics |
| title | Convolution-like structures, differential operators and diffusion processes |
| title_auth | Convolution-like structures, differential operators and diffusion processes |
| title_exact_search | Convolution-like structures, differential operators and diffusion processes |
| title_exact_search_txtP | Convolution-like structures, differential operators and diffusion processes |
| title_full | Convolution-like structures, differential operators and diffusion processes Rúben Sousa, Manuel Guerra, Semyon Yakubovich |
| title_fullStr | Convolution-like structures, differential operators and diffusion processes Rúben Sousa, Manuel Guerra, Semyon Yakubovich |
| title_full_unstemmed | Convolution-like structures, differential operators and diffusion processes Rúben Sousa, Manuel Guerra, Semyon Yakubovich |
| title_short | Convolution-like structures, differential operators and diffusion processes |
| title_sort | convolution like structures differential operators and diffusion processes |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033825260&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT sousaruben convolutionlikestructuresdifferentialoperatorsanddiffusionprocesses AT guerramanuel convolutionlikestructuresdifferentialoperatorsanddiffusionprocesses AT yakubovichsemyon convolutionlikestructuresdifferentialoperatorsanddiffusionprocesses |