Orthogonal polynomial systems and weighted Cesàro means:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2014
|
| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20140325-1181077-0-6 Inhaltsverzeichnis |
| Beschreibung: | 127 S. |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
ACKNOWLEDGEMENTS 3
ZUSAMMENFASSUNG 5
ABSTRACT 7
CONTENTS 8
INTRODUCTION 11
1 BASICS FROM ORTHOGONAL POLYNOMIALS AND OPERATOR THEORY 15
1.1 ELEMENTARY THEORY OF ORTHOGONAL POLYNOMIALS 15
1.1.1 MOMENT FUNCTIONAL AND ORTHOGONALITY 15
1.1.2 RECURRENCE RELATION AND FAVARD S THEOREM 18
1.1.3 ZEROS 19
1.1.4 ORTHOGONALITY WRT BOREL MEASURES AND REPRESENTATION THEOREM ... 20
1.2 OPERATOR AND SPECTRAL THEORY 22
1.2.1 NORMAL OPERATORS 22
1.2.2 SPECTRUM AND NUMERICAL RANGE 23
1.2.3 COMPACT OPERATORS 26
2 THE CONJUGATE ORTHOGONAL POLYNOMIAL SYSTEM 29
2.1 THE CONJUGATE SERIES FOR JACOBI POLYNOMIALS 30
2.2 TWO RELATED ORTHOGONAL SYSTEMS 34
2.2.1 ORTHOGONAL POLYNOMIAL SYSTEM WITH RESPECT TO /
J
,~ 35
2.2.2 ORTHOGONAL POLYNOMIAL SYSTEM WITH RESPECT TO FJ,
+
38
2.3 COMPUTATION OF THE CONJUGATE ORTHOGONAL POLYNOMIAL SYSTEM 43
2.3.1 A GENERAL FORMULA 43
2.3.2 THE SYMMETRIC CASE 47
2.4 PROPERTIES OF THE FUNCTION SPACES AND LP^*) 52
3 THE CESARO OPERATOR IN WEIGHTED SEQUENCE SPACES 55
3.1 BOUNDEDNESS OF THE CESARO OPERATOR IN ??{H) 56
3.1.1 HARDY S INEQUALITY 56
3.1.2 THE NORM OF THE CESARO OPERATOR 57
3.2 THE SPECTRUM OF THE WEIGHTED CESARO OPERATOR 60
3.3 CESARO OPERATOR AND THE GENERALIZED CONCEPTS OF NORMALITY 64
3.3.1 CLASSES OF OPERATORS WITH A WEAK NORMALITY CONDITION 64
9
HTTP://D-NB.INFO/1051383897
CONTENTS
3.3.2 HYPONORMALITY OF THE CESARO OPERATOR IN FT(H) 65
3.3.3 NECESSARY CONDITIONS FOR PARANORMAL AND NORMALOID CESARO OPERA
TORS IN
2
(H) 73
3.3.4 THE WEIGHTED CESARO OPERATOR AND QUASINORMALITY 76
3.4 REMARKS ON THE CESARO OPERATOR IN AND C 77
4 RELATIONS BETWEEN THE CESARO OPERATOR, ORTHOGONAL POLYNOMIAL SYSTEMS
AND
THE CONJUGATE ORTHOGONAL POLYNOMIAL SYSTEM 79
4.1 CESARO OPERATOR AND THE SYSTEM (R~(X))
NE
N
0
79
4.2 ON THE SPECTRUM OF TRIDIAGONAL OPERATORS 80
4.2.1 THE TRIDIAGONAL OPERATOR T 80
4.2.2 A CHARACTERIZATION OF 1 * S 82
4.2.3 INFERENCES ON THE SPECTRUM OF T
2
89
4.3 HYPONORMALITY AND THE ORTHOGONAL POLYNOMIAL SYSTEM 97
5 EXAMPLES: POLYNOMIALS RELATED TO HOMOGENEOUS TREES AND KARLIN-MCGREGOR
POLYNOMIALS 101
5.1 POLYNOMIALS RELATED TO HOMOGENEOUS TREES 101
5.1.1 THE CONJUGATE SYSTEM AND THE RELATED SYSTEMS OF POLYNOMIALS RE
LATED TO HOMOGENEOUS TREES 102
5.1.2 INFERENCES ON THE PROPERTIES OF THE POLYNOMIAL SYSTEMS AND THE
COR
RESPONDING CESARO OPERATORS 105
5.2 KARLIN-MCGREGOR POLYNOMIALS 108
5.2.1 THE CONJUGATE SYSTEM AND THE RELATED SYSTEMS OF KARLIN-MCGREGOR
POLYNOMIALS 110
5.2.2 INFERENCES ON THE PROPERTIES OF THE CORRESPONDING CESARO OPERATORS
. ILL
OUTLOOK 121
BIBLIOGRAPHY 127
10
|
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| discipline | Mathematik |
| format | Thesis Book |
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| spelling | Wagner, Julia Maria Verfasser aut Orthogonal polynomial systems and weighted Cesàro means Julia Maria Wagner 2014 127 S. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2014 Mit einer Zssfassung in dt. Sprache Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Cesàro-Mittel (DE-588)4147511-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Orthogonale Polynome (DE-588)4172863-4 s Cesàro-Mittel (DE-588)4147511-2 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20140325-1181077-0-6 http://mediatum.ub.tum.de/node?id=1181077 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20140325-1181077-0-6 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027238434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wagner, Julia Maria Orthogonal polynomial systems and weighted Cesàro means Orthogonale Polynome (DE-588)4172863-4 gnd Cesàro-Mittel (DE-588)4147511-2 gnd |
| subject_GND | (DE-588)4172863-4 (DE-588)4147511-2 (DE-588)4113937-9 |
| title | Orthogonal polynomial systems and weighted Cesàro means |
| title_auth | Orthogonal polynomial systems and weighted Cesàro means |
| title_exact_search | Orthogonal polynomial systems and weighted Cesàro means |
| title_full | Orthogonal polynomial systems and weighted Cesàro means Julia Maria Wagner |
| title_fullStr | Orthogonal polynomial systems and weighted Cesàro means Julia Maria Wagner |
| title_full_unstemmed | Orthogonal polynomial systems and weighted Cesàro means Julia Maria Wagner |
| title_short | Orthogonal polynomial systems and weighted Cesàro means |
| title_sort | orthogonal polynomial systems and weighted cesaro means |
| topic | Orthogonale Polynome (DE-588)4172863-4 gnd Cesàro-Mittel (DE-588)4147511-2 gnd |
| topic_facet | Orthogonale Polynome Cesàro-Mittel Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1181077 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20140325-1181077-0-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027238434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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