Harmonic analysis on exponential solvable Lie groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Tokyo [u.a.]
Springer
2015
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9784431552871 9784431552888 |
| DOI: | 10.1007/978-4-431-55288-8 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804152842843324417 |
|---|---|
| adam_text | HARMONIC ANALYSIS ON EXPONENTIAL SOLVABLE LIE GROUPS
/ FUJIWARA, HIDENORI
: 2015
ABSTRACT / INHALTSTEXT
THIS BOOK IS THE FIRST ONE THAT BRINGS TOGETHER RECENT RESULTS ON THE
HARMONIC ANALYSIS OF EXPONENTIAL SOLVABLE LIE GROUPS. THERE STILL ARE
MANY INTERESTING OPEN PROBLEMS, AND THE BOOK CONTRIBUTES TO THE FUTURE
PROGRESS OF THIS RESEARCH FIELD. AS WELL, VARIOUS RELATED TOPICS ARE
PRESENTED TO MOTIVATE YOUNG RESEARCHERS. THE ORBIT METHOD INVENTED BY
KIRILLOV IS APPLIED TO STUDY BASIC PROBLEMS IN THE ANALYSIS ON
EXPONENTIAL SOLVABLE LIE GROUPS. THIS METHOD TELLS US THAT THE UNITARY
DUAL OF THESE GROUPS IS REALIZED AS THE SPACE OF THEIR COADJOINT ORBITS.
THIS FACT IS ESTABLISHED USING THE MACKEY THEORY FOR INDUCED
REPRESENTATIONS, AND THAT MECHANISM IS EXPLAINED FIRST. ONE OF THE
FUNDAMENTAL PROBLEMS IN THE REPRESENTATION THEORY IS THE IRREDUCIBLE
DECOMPOSITION OF INDUCED OR RESTRICTED REPRESENTATIONS. THEREFORE, THESE
DECOMPOSITIONS ARE STUDIED IN DETAIL BEFORE PROCEEDING TO VARIOUS
RELATED PROBLEMS: THE MULTIPLICITY FORMULA, PLANCHEREL FORMULAS,
INTERTWINING OPERATORS, FROBENIUS RECIPROCITY, AND ASSOCIATED ALGEBRAS
OF INVARIANT DIFFERENTIAL OPERATORS. THE MAIN REASONING IN THE PROOF OF
THE ASSERTIONS MADE HERE IS INDUCTION, AND FOR THIS THERE ARE NOT MANY
TOOLS AVAILABLE. THUS A DETAILED ANALYSIS OF THE OBJECTS LISTED ABOVE IS
DIFFICULT EVEN FOR EXPONENTIAL SOLVABLE LIE GROUPS, AND IT IS OFTEN
ASSUMED THAT THE GROUP IS NILPOTENT. TO MAKE THE SITUATION CLEARER AND
FUTURE DEVELOPMENT POSSIBLE, MANY CONCRETE EXAMPLES ARE PROVIDED.
VARIOUS TOPICS PRESENTED IN THE NILPOTENT CASE STILL HAVE TO BE STUDIED
FOR SOLVABLE LIE GROUPS THAT ARE NOT NILPOTENT. THEY ALL PRESENT
INTERESTING AND IMPORTANT BUT DIFFICULT PROBLEMS, HOWEVER, WHICH SHOULD
BE ADDRESSED IN THE NEAR FUTURE. BEYOND THE EXPONENTIAL CASE,
HOLOMORPHICALLY INDUCED REPRESENTATIONS INTRODUCED BY AUSLANDER AND
KOSTANT ARE NEEDED, AND FOR THAT REASON THEY ARE INCLUDED IN THIS BOOK.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Fujiwara, Hidenori Ludwig, Jean 1947- |
| author_GND | (DE-588)1065249330 (DE-588)172241413 |
| author_facet | Fujiwara, Hidenori Ludwig, Jean 1947- |
| author_role | aut aut |
| author_sort | Fujiwara, Hidenori |
| author_variant | h f hf j l jl |
| building | Verbundindex |
| bvnumber | BV042279111 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)899163363 (DE-599)DNB1063237793 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-4-431-55288-8 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:17:09Z |
| institution | BVB |
| isbn | 9784431552871 9784431552888 |
| language | English |
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| spelling | Fujiwara, Hidenori Verfasser (DE-588)1065249330 aut Harmonic analysis on exponential solvable Lie groups Hidenori Fujiwara ; Jean Ludwig Tokyo [u.a.] Springer 2015 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Springer monographs in mathematics Electronic book text Ludwig, Jean 1947- Verfasser (DE-588)172241413 aut https://doi.org/10.1007/978-4-431-55288-8 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027716507&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Fujiwara, Hidenori Ludwig, Jean 1947- Harmonic analysis on exponential solvable Lie groups |
| title | Harmonic analysis on exponential solvable Lie groups |
| title_auth | Harmonic analysis on exponential solvable Lie groups |
| title_exact_search | Harmonic analysis on exponential solvable Lie groups |
| title_full | Harmonic analysis on exponential solvable Lie groups Hidenori Fujiwara ; Jean Ludwig |
| title_fullStr | Harmonic analysis on exponential solvable Lie groups Hidenori Fujiwara ; Jean Ludwig |
| title_full_unstemmed | Harmonic analysis on exponential solvable Lie groups Hidenori Fujiwara ; Jean Ludwig |
| title_short | Harmonic analysis on exponential solvable Lie groups |
| title_sort | harmonic analysis on exponential solvable lie groups |
| url | https://doi.org/10.1007/978-4-431-55288-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027716507&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fujiwarahidenori harmonicanalysisonexponentialsolvableliegroups AT ludwigjean harmonicanalysisonexponentialsolvableliegroups |