Spherical inversion on SL n (R):
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 411 - 417 |
| Beschreibung: | XX, 426 S. 24 cm |
| ISBN: | 0387951156 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV013927543 | ||
| 003 | DE-604 | ||
| 005 | 20050727 | ||
| 007 | t | ||
| 008 | 010918s2001 gw |||| |||| 00||| eng d | ||
| 016 | 7 | |a 962204315 |2 DE-101 | |
| 020 | |a 0387951156 |9 0-387-95115-6 | ||
| 035 | |a (OCoLC)44592776 | ||
| 035 | |a (DE-599)BVBBV013927543 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-20 |a DE-824 |a DE-355 |a DE-91G |a DE-384 |a DE-29T |a DE-634 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA406 | |
| 082 | 0 | |a 515/.53 |2 21 | |
| 084 | |a SK 340 |0 (DE-625)143232: |2 rvk | ||
| 084 | |a MAT 337f |2 stub | ||
| 084 | |a MAT 225f |2 stub | ||
| 100 | 1 | |a Jorgenson, Jay |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Spherical inversion on SL n (R) |c Jay Jorgenson ; Serge Lang |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a XX, 426 S. |b 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Literaturverz. S. 411 - 417 | ||
| 650 | 4 | |a Décomposition (Mathématiques) | |
| 650 | 4 | |a Fonctions sphériques | |
| 650 | 7 | |a Lie-groepen |2 gtt | |
| 650 | 4 | |a Decomposition (Mathematics) | |
| 650 | 4 | |a Spherical functions | |
| 650 | 0 | 7 | |a Kugelfunktion |0 (DE-588)4033494-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Halbeinfache Lie-Gruppe |0 (DE-588)4122188-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inversion |g Mathematik |0 (DE-588)4162235-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Halbeinfache Lie-Gruppe |0 (DE-588)4122188-6 |D s |
| 689 | 0 | 1 | |a Kugelfunktion |0 (DE-588)4033494-6 |D s |
| 689 | 0 | 2 | |a Inversion |g Mathematik |0 (DE-588)4162235-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Lang, Serge |d 1927-2005 |e Verfasser |0 (DE-588)119305119 |4 aut | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009530879&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009530879 | ||
Datensatz im Suchindex
| _version_ | 1804128773153488896 |
|---|---|
| adam_text | JAY JORGENSON SERGE LANG SPHERICAL INVERSION ON SL N (R) SPRINGER
CONTENTS ACKNOWLEDGMENTS IX OVERVIEW XI TABLE OF THE DECOMPOSITIONS XVII
CHAPTER I IWASAWA DECOMPOSITION AND POSITIVITY 1 §1. THE IWASAWA
DECOMPOSITION 1 §2. HAAR MEASURE AND IWASAWA DECOMPOSITION 5 §3. THE
CARTAN LIE DECOMPOSITION, POLYNOMIAL ALGEBRA AND CHEVALLEY S THEOREM 10
§4. POSITIVITY 17 §5. CONVEXITY 25 §6. THE HARISH-CHANDRA [/-POLAR
INEQUALITY; CONNECTION WITH THE IWASAWA AND POLAR DECOMPOSITIONS 28
CHAPTER II INVARIANT DIFFERENTIAL OPERATORS AND THE IWASAWA DIRECT IMAGE
33 §1. INVARIANT DIFFERENTIAL OPERATORS ON A LIE GROUP 36 §2. THE
PROJECTION ON A HOMOGENEOUS SPACE 44 §3. THE IWASAWA PROJECTION ON A 51
§4. USE OF THE CARTAN LIE DECOMPOSITION 57 §5. THE HARISH-CHANDRA
TRANSFORMS 59 §6. THE TRANSPOSE AND INVOLUTION 66 VI CONTENTS C H A P T
E R II! CHARACTERS, EIGENFUNCTIONS, SPHERICAL KERNEL AND W-LNVARIANCE
.... 75 §1. CHARACTERS 75 §2. THE (A, N)-CHARACTERS AND THE IWASAWA
CHARACTER 83 §3. THE WEYL GROUP 87 §4. ORBITAL INTEGRAL FOR THE HARISH
TRANSFORM 91 §5. W-INVARIANCE OF THE HARISH AND SPHERICAL TRANSFORMS 98
§6. A -BI-INVARIANT FUNCTIONS AND UNIQUENESS OF SPHERICAL FUNCTIONS . .
. . 105 §7. INTEGRATION FORMULAS AND THE MAP X I-» X~ L 108 §8.
W-HARMONIC POLYNOMIALS AND EIGENFUNCTIONS OF ^-INVARIANT DIFFERENTIAL
OPERATORS ON A 114 CHAPTER IV CONVOLUTIONS, SPHERICAL FUNCTIONS AND THE
MELLIN TRANSFORM 131 §1. WEAKLY SYMMETRIC SPACES 132 §2. CHARACTERS AND
CONVOLUTION OPERATORS 138 §3. EXAMPLE: THE GAMMA FUNCTION 141 §4.
-INVARIANCE OR BI-INVARIANCE AND EIGENFUNCTIONS OF CONVOLUTIONS . . . .
143 §5. CONVOLUTION SPHERICALITY 148 §6. THE SPHERICAL TRANSFORM AS
MULTIPLICATIVE HOMOMORPHISM 155 §7. THE MELLIN TRANSFORM AND THE
PALEY-WIENER SPACE 159 §8. BEHAVIOR OF THE SUPPORT 167 CHAPTER V
GELFAND-NAIMARK DECOMPOSITION AND THE HARISH-CHANDRA C-FUNCTION . 177
§1. THE GELFAND-NAIMARK DECOMPOSITION AND THE HARISH-CHANDRA MAPPING OF
U INTO M K 178 §2. THE BRUHAT DECOMPOSITION 181 §3. JACOBIAN FORMULAS
187 §4. INTEGRAL FORMULAS FOR SPHERICAL FUNCTIONS 195 §5. THE C-FUNCTION
AND THE FIRST SPHERICAL ASYMPTOTICS 197 §6. THE BHANU-MURTY FORMULA FOR
THE C-FUNCTION 204 §7. INVARIANT FORMULATION ON O^ 209 §8. COROLLARIES
ON THE ANALYTIC BEHAVIOR OF C HA R 214 CHAPTER VI POLAR DECOMPOSITION
219 §1. THE JACOBIAN OF THE POLAR MAP 219 §2. FROM /IF-BI-INVARIANT
FUNCTIONS ON G TO ^-INVARIANT FUNCTIONS ON A . . 233 APPENDIX. THE
BERNSTEIN CALCULUS LEMMA 237 §3. PULLING BACK CHARACTERS AND SPHERICAL
FUNCTIONS TO A 243 §4. LEMMAS USING THE SEMISIMPLE LIE IWASAWA
DECOMPOSITION 246 §5. THE TRANSPOSE IWASAWA DECOMPOSITION AND POLAR
DIRECT IMAGE 248 §6. W-INVARIANTS 253 CONTENTS VII CHAPTER VLL THE
CASIMIR OPERATOR 255 §1. BILINEAR FORMS OF CARTAN TYPE 256 §2. THE
CASIMIR DIFFERENTIAL OPERATOR 260 §3. THE A-IWASAWA AND HARISH-CHANDRA
DIRECT IMAGES 262 §4. THE POLAR DIRECT IMAGE 270 CHAPTER VIII THE
HARISH-CHANDRA SERIES AND SPHERICAL INVERSION 277 §0. LINEAR
INDEPENDENCE OF CHARACTERS REVISITED 277 §1. EIGENFUNCTIONS OF CASIMIR
280 §2. THE HARISH-CHANDRA SERIES AND GANGOLLI ESTIMATE 284 §3. THE
C-FUNCTION AND THE W-TRACE 293 §4. THE HELGASON AND ANKER SUPPORT
THEOREMS 298 §5. AN L 2 -ESTIMATE AND LIMIT 301 §6. SPHERICAL INVERSION
304 CHAPTER IX GENERAL INVERSION THEOREMS 30 9 §1. THE ROSENBERG
ARGUMENTS 311 §2. HELGASON INVERSION ON PALEY-WIENER AND THE L 2
-ISOMETRY 320 §3. THE CONSTANT IN THE INVERSION FORMULA 321 CHAPTER X
THE HARISH-CHANDRA SCHWARTZ SPACE (HCS) AND ANKER S PROOF OF INVERSION
325 §1. MORE HARISH-CHANDRA CONVEXITY INEQUALITIES 326 §2. MORE
HARISH-CHANDRA INEQUALITIES FOR SPHERICAL FUNCTIONS 332 §3. THE
HARISH-CHANDRA SCHWARTZ SPACE 339 §4. SCHWARTZ CONTINUITY OF THE
SPHERICAL TRANSFORM 351 §5. CONTINUITY OF THE INVERSE TRANSFORM AND
SPHERICAL INVERSION ON HCS(K G/K) 355 §6. EXTENSION OF FORMULAS BY HCS
CONTINUITY 361 §7. AN EXAMPLE: THE HEAT KERNEL 365 §8. THE HARISH
TRANSFORM 367 CHAPTER XI TUBE DOMAINS AND THE L 1 (EVEN L P ) HCS SPACES
373 §1. THE SCHWARTZ SPACE ON TUBES 374 §2. THE FILTRATION HCS (P)
(K G/K) WITH 0 P ^ 2 377 §3. THE INVERSE TRANSFORM 381 §4. BOUNDED
SPHERICAL FUNCTIONS 384 §5. BACK TO THE HEAT KERNEL 385 VIII CONTENTS
CHAPTER XII SL N (C) 387 §1. A FORMULA OF EXPONENTIAL POLYNOMIALS 388
§2. CHARACTERS AND JACOBIANS 392 §3. THE POLAR DIRECT IMAGE 396 §4.
SPHERICAL FUNCTIONS AND INVERSION 398 §5. THE HEAT KERNEL 402 §6. THE
FLENSTED-JENSEN DECOMPOSITION AND REDUCTION 406 BIBLIOGRAPHY 411 TABLE
OF NOTATION 419 INDEX 423
|
| any_adam_object | 1 |
| author | Jorgenson, Jay Lang, Serge 1927-2005 |
| author_GND | (DE-588)119305119 |
| author_facet | Jorgenson, Jay Lang, Serge 1927-2005 |
| author_role | aut aut |
| author_sort | Jorgenson, Jay |
| author_variant | j j jj s l sl |
| building | Verbundindex |
| bvnumber | BV013927543 |
| callnumber-first | Q - Science |
| callnumber-label | QA406 |
| callnumber-raw | QA406 |
| callnumber-search | QA406 |
| callnumber-sort | QA 3406 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 |
| classification_tum | MAT 337f MAT 225f |
| ctrlnum | (OCoLC)44592776 (DE-599)BVBBV013927543 |
| dewey-full | 515/.53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.53 |
| dewey-search | 515/.53 |
| dewey-sort | 3515 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02002nam a2200529 c 4500</leader><controlfield tag="001">BV013927543</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20050727 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010918s2001 gw |||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">962204315</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387951156</subfield><subfield code="9">0-387-95115-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)44592776</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013927543</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA406</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.53</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 340</subfield><subfield code="0">(DE-625)143232:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 337f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 225f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jorgenson, Jay</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Spherical inversion on SL n (R)</subfield><subfield code="c">Jay Jorgenson ; Serge Lang</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XX, 426 S.</subfield><subfield code="b">24 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Springer monographs in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 411 - 417</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Décomposition (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fonctions sphériques</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Lie-groepen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Decomposition (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Spherical functions</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kugelfunktion</subfield><subfield code="0">(DE-588)4033494-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Halbeinfache Lie-Gruppe</subfield><subfield code="0">(DE-588)4122188-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Inversion</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4162235-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Halbeinfache Lie-Gruppe</subfield><subfield code="0">(DE-588)4122188-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Kugelfunktion</subfield><subfield code="0">(DE-588)4033494-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Inversion</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4162235-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lang, Serge</subfield><subfield code="d">1927-2005</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)119305119</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009530879&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009530879</subfield></datafield></record></collection> |
| id | DE-604.BV013927543 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:54:34Z |
| institution | BVB |
| isbn | 0387951156 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009530879 |
| oclc_num | 44592776 |
| open_access_boolean | |
| owner | DE-20 DE-824 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-384 DE-29T DE-634 DE-11 DE-188 |
| owner_facet | DE-20 DE-824 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-384 DE-29T DE-634 DE-11 DE-188 |
| physical | XX, 426 S. 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Jorgenson, Jay Verfasser aut Spherical inversion on SL n (R) Jay Jorgenson ; Serge Lang New York [u.a.] Springer 2001 XX, 426 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 411 - 417 Décomposition (Mathématiques) Fonctions sphériques Lie-groepen gtt Decomposition (Mathematics) Spherical functions Kugelfunktion (DE-588)4033494-6 gnd rswk-swf Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd rswk-swf Inversion Mathematik (DE-588)4162235-2 gnd rswk-swf Halbeinfache Lie-Gruppe (DE-588)4122188-6 s Kugelfunktion (DE-588)4033494-6 s Inversion Mathematik (DE-588)4162235-2 s DE-604 Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009530879&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jorgenson, Jay Lang, Serge 1927-2005 Spherical inversion on SL n (R) Décomposition (Mathématiques) Fonctions sphériques Lie-groepen gtt Decomposition (Mathematics) Spherical functions Kugelfunktion (DE-588)4033494-6 gnd Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd Inversion Mathematik (DE-588)4162235-2 gnd |
| subject_GND | (DE-588)4033494-6 (DE-588)4122188-6 (DE-588)4162235-2 |
| title | Spherical inversion on SL n (R) |
| title_auth | Spherical inversion on SL n (R) |
| title_exact_search | Spherical inversion on SL n (R) |
| title_full | Spherical inversion on SL n (R) Jay Jorgenson ; Serge Lang |
| title_fullStr | Spherical inversion on SL n (R) Jay Jorgenson ; Serge Lang |
| title_full_unstemmed | Spherical inversion on SL n (R) Jay Jorgenson ; Serge Lang |
| title_short | Spherical inversion on SL n (R) |
| title_sort | spherical inversion on sl n r |
| topic | Décomposition (Mathématiques) Fonctions sphériques Lie-groepen gtt Decomposition (Mathematics) Spherical functions Kugelfunktion (DE-588)4033494-6 gnd Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd Inversion Mathematik (DE-588)4162235-2 gnd |
| topic_facet | Décomposition (Mathématiques) Fonctions sphériques Lie-groepen Decomposition (Mathematics) Spherical functions Kugelfunktion Halbeinfache Lie-Gruppe Inversion Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009530879&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jorgensonjay sphericalinversiononslnr AT langserge sphericalinversiononslnr |