Harmonic analysis in hypercomplex systems:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1998
|
| Schriftenreihe: | Mathematics and its applications
434 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008221051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 483 S. graph. Darst. |
| ISBN: | 0792350294 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV012137902 | ||
| 003 | DE-604 | ||
| 005 | 19990415 | ||
| 007 | t| | ||
| 008 | 980904s1998 xx d||| |||| 00||| eng d | ||
| 020 | |a 0792350294 |9 0-7923-5029-4 | ||
| 035 | |a (OCoLC)246724177 | ||
| 035 | |a (DE-599)BVBBV012137902 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-824 |a DE-703 |a DE-11 | ||
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a MAT 430f |2 stub | ||
| 100 | 1 | |a Berezanskij, Jurij M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Harmonic analysis in hypercomplex systems |c by Yu. M. Berezansky and A. A. Kalyuzhnyi |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1998 | |
| 300 | |a X, 483 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 434 | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Systemtheorie |0 (DE-588)4058812-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | 1 | |a Systemtheorie |0 (DE-588)4058812-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kalyuzhnyi, A. A. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematics and its applications |v 434 |w (DE-604)BV008163334 |9 434 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008221051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008221051 | |
Datensatz im Suchindex
| _version_ | 1819371130234863616 |
|---|---|
| adam_text | COIlTEnTS
Preface to the English Edition jx
Introduction 1
Chapter 1. GENERAL THEORY OF HYPERCOMPLEX SYSTEMS 7
1. Fundamental Concepts of the Theory of Hypercomplex Systems
with Locally Compact Basis 8
1.1. Definition of Hypercomplex Systems. Characters 8
1.2. Theorem of Existence of a Multiplicative Measure 15
1.3. Normal Hypercomplex Systems 20
1.4. Normal Hypercomplex Systems with Basis Unity 28
1.5. Even Subsystem of a Normal Hypercomplex System 32
1.6. The Case of a Discrete Basis 34
1.7. Hilbert Algebras 37
1.8. Parameter Depending Measures 39
2. Hypercomplex Systems and Related Objects 42
2.1. Generalized Translation Operators and Hypercomplex Systems 42
2.2. Strong Invariance of Invariant Measures 55
2.3. Hypergroups and Hypercomplex Systems 60
2.4. Hypercomplex Systems Whose Structure Measure Is Not
Necessarily Nonnegative 63
2.5. Convolution Algebras and Hypercomplex Systems 66
3. Elements of Harmonic Analysis for Normal Hypercomplex Systems
with Basis Unity 69
3.1. Fourier Transformation and the Plancherel Theorem 69
3.2. Duality of Commutative Hypercomplex Systems 83
v
vi Contents
3.3. The Case of Discrete Hypercomplex Systems 99
3.4. Representations of Hypercomplex Systems and Approximation
Theorem 105
4. Hypercomplex Subsystems and Homomorphisms 121
4.1. Definition of Hypercomplex Subsystems 121
4.2. Fundamental Properties of Hypercomplex Subsystems 126
4.3. Homomorphisms 128
4.4. Direct and Semidirect Products of Hypercomplex Systems.
Join of Hypercomplex Systems 133
5. Further Generalizations of Hypercomplex Systems 138
5.1. Properties of Hilbert Bialgebras 139
5.2. Quantized Hypercomplex Systems 142
5.3. Harmonic Analysis in Quantized Hypercomplex Systems
with One Commutative Operation 157
5.4. Real Hypercomplex Systems with Compact and Discrete Bases 161
Chapter 2. EXAMPLES OF HYPERCOMPLEX SYSTEMS 165
1. Centers of Group Algebras of Compact Groups 165
1.1. General Construction of Hypercomplex Systems Corresponding to
Locally Compact Groups 166
1.2. Centers of Group Algebras of Compact Groups 167
1.3. Elements of the Theory of Representations of Compact Groups 168
1.4. Peter Weyl Theorem 174
1.5. Tannaka M.Krein Duality Theorem 180
1.6. Elements of the Theory of Semisimple Groups and Lie Algebras 189
1.7. Center of the Group Algebra of Compact Semisimple Lie Groups 202
1.8. Algebra 0 of Equivalence Classes of Irreducible Representations
of a Compact Semisimple Lie Group G 217
2. Gelfand Pairs 223
2.1. Definition of Gelfand Pairs 223
2.2. Spherical Functions 227
2.3. Representations of Class I 232
2.4. Harmonic Analysis on Gelfand Pairs 237
2.5. Hypercomplex Systems Associated With the Delsarte Generalized
Translation Operators 246
2.6. Center of Group Algebra as a Gelfand Pair 249
Contents vii
3. Orthogonal Polynomials 250
3.1. Discrete Hypercomplex Systems Associated with Orthogonal
Systems of Polynomials 250
3.2. Jacobian Matrices and Generalized Translation Operators 254
3.3. Characterization of Hypercomplex Systems Associated with
Orthogonal Polynomials 256
3.4. Another Method for the Construction of a Hypercomplex System
Associated with Orthogonal Polynomials. Examples 259
3.5. Compact Hypercomplex Systems Associated with Orthogonal
Polynomials 265
3.6. The Case of Not Necessarily Nonnegative Structure Constants 272
3.7. Examples of Hypercomplex Systems with Real Structure Constants 275
3.8. Transmutation Operators 280
4. Hypercomplex Systems Constructed for the Sturm Liouville Equation 284
4.1. Riemann Function 284
4.2. Hypercomplex Systems Constructed for the Sturm Liouville
Equation 289
4.3. Structure Measure Which Is Not Necessarily Nonnegative 295
4.4 Set of Characters of the Hypercomplex System Associated with the
Sturm Liouville Equation 302
4.5. Survey of Related Results 311
Chapter 3. ELEMENTS OF LIE THEORY FOR GENERALIZED
TRANSLATION OPERATORS 315
1. Basic Concepts 316
1.1. Hypergroup Algebra of Infinitely Differentiable Generalized Translation
Operators 317
1.2. Topological Bialgebras 322
1.3. Infinitesimal Object for Generalized Translation Operators 324
1.4. General Properties of Generators of Generalized Translation
Operators 330
1.5. Algebraic Approach to the Infinitesimal Theory of Formal Generalized
Translation Operators 334
1.6. Some Facts from the Theory of Topological Vector Spaces 338
2. Analog of Lie Theory for Some Classes of Generalized
Translation Operators 341
2.1. Infinitesimal Object For the Delsarte Generalized Translation
Operators 341
viii Contents
2.2. Delsarte Type Generalized Translation Operators and Generalized
Lie Algebras 359
2.3. Infinitesimal Algebra of the Hypercomplex System LX{G,H) 367
3. Duality of Generators of One Dimensional Compact and Discrete
Hypercomplex Systems 372
3.1. Generators of One Dimensional Compact and Discrete Hypercomplex
Systems 372
3.2. General Case of the Construction of Generalized Translation
Operators from a Generator 389
3.3. Analog of the Canonical Commutation Relations for the Delsarte
Generalized Translation Operators 396
Supplement. Hypercomplex Systems and Hypergroups:
Connections and Distinctions 405
1. Hypercomplex Systems with Locally Compact Basis.
Definition and Properties 405
2. Examples of Hypercomplex Systems 415
3. Harmonic Analysis in the Locally Compact Case 419
4. Hypergroups and Hypercomplex Systems 424
5. Generalizations 426
6. Remarks on Terminology 428
Bibliographical Notes 431
References 439
Subject Index 481
|
| any_adam_object | 1 |
| author | Berezanskij, Jurij M. Kalyuzhnyi, A. A. |
| author_facet | Berezanskij, Jurij M. Kalyuzhnyi, A. A. |
| author_role | aut aut |
| author_sort | Berezanskij, Jurij M. |
| author_variant | j m b jm jmb a a k aa aak |
| building | Verbundindex |
| bvnumber | BV012137902 |
| classification_rvk | SK 450 |
| classification_tum | MAT 430f |
| ctrlnum | (OCoLC)246724177 (DE-599)BVBBV012137902 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01553nam a2200385 cb4500</leader><controlfield tag="001">BV012137902</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19990415 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">980904s1998 xx d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792350294</subfield><subfield code="9">0-7923-5029-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246724177</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012137902</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="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 430f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Berezanskij, Jurij M.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Harmonic analysis in hypercomplex systems</subfield><subfield code="c">by Yu. M. Berezansky and A. A. Kalyuzhnyi</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht [u.a.]</subfield><subfield code="b">Kluwer Acad. Publ.</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 483 S.</subfield><subfield code="b">graph. Darst.</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="1" ind2=" "><subfield code="a">Mathematics and its applications</subfield><subfield code="v">434</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Systemtheorie</subfield><subfield code="0">(DE-588)4058812-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Systemtheorie</subfield><subfield code="0">(DE-588)4058812-9</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">Kalyuzhnyi, A. A.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics and its applications</subfield><subfield code="v">434</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">434</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ 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=008221051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008221051</subfield></datafield></record></collection> |
| id | DE-604.BV012137902 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:25:00Z |
| institution | BVB |
| isbn | 0792350294 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008221051 |
| oclc_num | 246724177 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-703 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-703 DE-11 |
| physical | X, 483 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spellingShingle | Berezanskij, Jurij M. Kalyuzhnyi, A. A. Harmonic analysis in hypercomplex systems Mathematics and its applications Harmonische Analyse (DE-588)4023453-8 gnd Systemtheorie (DE-588)4058812-9 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4058812-9 |
| title | Harmonic analysis in hypercomplex systems |
| title_auth | Harmonic analysis in hypercomplex systems |
| title_exact_search | Harmonic analysis in hypercomplex systems |
| title_full | Harmonic analysis in hypercomplex systems by Yu. M. Berezansky and A. A. Kalyuzhnyi |
| title_fullStr | Harmonic analysis in hypercomplex systems by Yu. M. Berezansky and A. A. Kalyuzhnyi |
| title_full_unstemmed | Harmonic analysis in hypercomplex systems by Yu. M. Berezansky and A. A. Kalyuzhnyi |
| title_short | Harmonic analysis in hypercomplex systems |
| title_sort | harmonic analysis in hypercomplex systems |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd Systemtheorie (DE-588)4058812-9 gnd |
| topic_facet | Harmonische Analyse Systemtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008221051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT berezanskijjurijm harmonicanalysisinhypercomplexsystems AT kalyuzhnyiaa harmonicanalysisinhypercomplexsystems |