Regularised integrals, sums and traces: an analytic point of view
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Soc.
2012
|
| Schriftenreihe: | University lecture series
59 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | X, 190 S. |
| ISBN: | 9780821853672 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV040384185 | ||
| 003 | DE-604 | ||
| 005 | 20230821 | ||
| 007 | t | ||
| 008 | 120823s2012 xxu |||| 00||| eng d | ||
| 010 | |a 2012010029 | ||
| 020 | |a 9780821853672 |c alk. paper |9 978-0-8218-5367-2 | ||
| 035 | |a (OCoLC)815888275 | ||
| 035 | |a (DE-599)BVBBV040384185 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-188 |a DE-384 |a DE-355 |a DE-91G |a DE-19 |a DE-634 | ||
| 050 | 0 | |a QA351 | |
| 082 | 0 | |a 512.7/3 | |
| 084 | |a SI 165 |0 (DE-625)143085: |2 rvk | ||
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 084 | |a MAT 472f |2 stub | ||
| 084 | |a MAT 109f |2 stub | ||
| 084 | |a MAT 400f |2 stub | ||
| 100 | 1 | |a Paycha, Sylvie |d 1960- |e Verfasser |0 (DE-588)115402748 |4 aut | |
| 245 | 1 | 0 | |a Regularised integrals, sums and traces |b an analytic point of view |c Sylvie Paycha |
| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 2012 | |
| 300 | |a X, 190 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a University lecture series |v 59 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Functions, Zeta | |
| 650 | 4 | |a L-functions | |
| 650 | 4 | |a Convergence | |
| 650 | 4 | |a Integrals | |
| 650 | 7 | |a Number theory -- Zeta and L-functions: analytic theory -- \zeta (s) and L(s, \chi) |2 msc | |
| 650 | 7 | |a Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of integrals |2 msc | |
| 650 | 7 | |a Operator theory -- Linear spaces and algebras of operators -- Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) |2 msc | |
| 650 | 7 | |a Quantum theory -- Quantum field theory; related classical field theories -- Anomalies |2 msc | |
| 650 | 7 | |a Numerical analysis -- Acceleration of convergence -- Euler-Maclaurin formula |2 msc | |
| 650 | 0 | 7 | |a Integral |0 (DE-588)4131477-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spur |g Mathematik |0 (DE-588)4202272-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Regularisierung |0 (DE-588)4124043-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Summierbarkeit |0 (DE-588)4294383-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Regularisierung |0 (DE-588)4124043-1 |D s |
| 689 | 0 | 1 | |a Integral |0 (DE-588)4131477-3 |D s |
| 689 | 0 | 2 | |a Spur |g Mathematik |0 (DE-588)4202272-1 |D s |
| 689 | 0 | 3 | |a Summierbarkeit |0 (DE-588)4294383-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-8218-9035-6 |
| 830 | 0 | |a University lecture series |v 59 |w (DE-604)BV004153846 |9 59 | |
| 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=025237647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025237647 | ||
Datensatz im Suchindex
| _version_ | 1804149427423674368 |
|---|---|
| adam_text | Titel: Regularised integrals, sums and traces
Autor: Paycha, Sylvie
Jahr: 2012
Contents
Preface
vn
Chapter 1. The Gamma function extended to
nonpositive integer points 1
1.1. Homogeneous distributions 1
1.2. A meromorphic extension of the Gamma function 4
1.3. Riesz regularisation 5
1.4. Hadamard s finite part method 7
1.5. Discrepancies 12
Chapter 2. The canonical integral
and noncommutative residue on symbols 15
2.1. Classical and log-polyhomogeneous symbols on Rd 15
2.2. The noncommutative residue on classical symbols 20
2.3. Closed linear forms on symbol valued forms 22
2.4. The noncommutative residue characterised via Stokes property. I 24
2.5. The canonical integral characterised via Stokes property. I 24
2.6. Characterisations by means of the translation invariance 28
2.7. The noncommutative residue characterised via its covariance. I 32
Chapter 3. The cut-off regularised integral 35
3.1. Cut-off (or Hadamard finite part) integral 35
3.2. Cut-off integrals and periods 38
3.3. Discrepancies of the cut-off integral 39
3.4. Characterisations by means of Stokes property. II 48
3.5. The canonical integral characterised by means of its covariance 49
Chapter 4. The noncommutative residue as a complex residue 53
4.1. Regularised evaluators 53
4.2. Meromorphic extensions of integrals on classical symbols 56
4.3. Extension to log-poly homogeneous symbols 61
4.4. Invariance properties of the noncommutative residue 68
4.5. Dimensional versus cut-off regularised integrals 70
4.6. Discrepancies of regularised integrals 74
Chapter 5. The canonical sum on noninteger order classical Symbols 79
5.1. The Euler-Maclaurin formula 79
5.2. The higher dimensional Euler-Maclaurin formula 83
5.3. Cut-off discrete sums on Zd subordinated to convex polytopes 86
5.4. Zd-translation invariant linear forms on symbols 91
5.5. The noncommutative residue and Zd-translation invariance 93
vi CONTENTS
5.6. Regularised discrete sums on symbols 95
5.7. Two special zeta functions 98
Chapter 6. Traces on pseudodifferential Operators 105
6.1. From symbols to Operators 105
6.2. Basic properties of pseudodifferential Operators 109
6.3. Pseudodifferential Operators on manifolds 114
6.4. From closed linear forms on symbols to traces on Operators 118
6.5. A first characterisation of the noncommutative residue 126
Chapter 7. Weighted traces 131
7.1. Complex powers 131
7.2. A fundamental formula 133
7.3. Zeta regularised traces 135
7.4. Logarithms of admissible Operators 136
7.5. Discrepancies 139
7.6. Characterising traces on Operators 141
Chapter 8. Logarithmic residues 145
8.1. Regularised traces-locality versus nonlocality 145
8.2. Application to ^-regularised traces 147
8.3. Traces of differentiable families 149
8.4. The residue determinant 155
8.5. The index as a superresidue 15
8.6. Application to the Atiyah-Singer index theorem-a toy model 160
Chapter 9. Anomalies of regularised determinants 167
9.1. Weighted and ^-determinants 167
9.2. Multiplicative anomaly of a weighted determinant 170
9.3. Multiplicative anomaly of the ^-determinant 173
9.4. Conformally covariant Operators 174
9.5. Conformal anomalies 176
9.6. Conformal anomaly of the ^-determinant 181
Bibliography 183
Index 189
|
| any_adam_object | 1 |
| author | Paycha, Sylvie 1960- |
| author_GND | (DE-588)115402748 |
| author_facet | Paycha, Sylvie 1960- |
| author_role | aut |
| author_sort | Paycha, Sylvie 1960- |
| author_variant | s p sp |
| building | Verbundindex |
| bvnumber | BV040384185 |
| callnumber-first | Q - Science |
| callnumber-label | QA351 |
| callnumber-raw | QA351 |
| callnumber-search | QA351 |
| callnumber-sort | QA 3351 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 165 SK 620 |
| classification_tum | MAT 472f MAT 109f MAT 400f |
| ctrlnum | (OCoLC)815888275 (DE-599)BVBBV040384185 |
| dewey-full | 512.7/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/3 |
| dewey-search | 512.7/3 |
| dewey-sort | 3512.7 13 |
| 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>02862nam a2200649 cb4500</leader><controlfield tag="001">BV040384185</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230821 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">120823s2012 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2012010029</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821853672</subfield><subfield code="c">alk. paper</subfield><subfield code="9">978-0-8218-5367-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)815888275</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV040384185</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA351</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.7/3</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 165</subfield><subfield code="0">(DE-625)143085:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 472f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 109f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 400f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Paycha, Sylvie</subfield><subfield code="d">1960-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)115402748</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Regularised integrals, sums and traces</subfield><subfield code="b">an analytic point of view</subfield><subfield code="c">Sylvie Paycha</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Soc.</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 190 S.</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">University lecture series</subfield><subfield code="v">59</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quantentheorie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions, Zeta</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">L-functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convergence</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integrals</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Number theory -- Zeta and L-functions: analytic theory -- \zeta (s) and L(s, \chi)</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of integrals</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Operator theory -- Linear spaces and algebras of operators -- Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Quantum theory -- Quantum field theory; related classical field theories -- Anomalies</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Numerical analysis -- Acceleration of convergence -- Euler-Maclaurin formula</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integral</subfield><subfield code="0">(DE-588)4131477-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Spur</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4202272-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Regularisierung</subfield><subfield code="0">(DE-588)4124043-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Summierbarkeit</subfield><subfield code="0">(DE-588)4294383-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Regularisierung</subfield><subfield code="0">(DE-588)4124043-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Integral</subfield><subfield code="0">(DE-588)4131477-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Spur</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4202272-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Summierbarkeit</subfield><subfield code="0">(DE-588)4294383-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-0-8218-9035-6</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">University lecture series</subfield><subfield code="v">59</subfield><subfield code="w">(DE-604)BV004153846</subfield><subfield code="9">59</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=025237647&sequence=000002&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:BVB01-025237647</subfield></datafield></record></collection> |
| id | DE-604.BV040384185 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:22:51Z |
| institution | BVB |
| isbn | 9780821853672 |
| language | English |
| lccn | 2012010029 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025237647 |
| oclc_num | 815888275 |
| open_access_boolean | |
| owner | DE-188 DE-384 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 |
| owner_facet | DE-188 DE-384 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 |
| physical | X, 190 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Paycha, Sylvie 1960- Verfasser (DE-588)115402748 aut Regularised integrals, sums and traces an analytic point of view Sylvie Paycha Providence, RI American Mathematical Soc. 2012 X, 190 S. txt rdacontent n rdamedia nc rdacarrier University lecture series 59 Includes bibliographical references and index Quantentheorie Functions, Zeta L-functions Convergence Integrals Number theory -- Zeta and L-functions: analytic theory -- \zeta (s) and L(s, \chi) msc Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of integrals msc Operator theory -- Linear spaces and algebras of operators -- Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) msc Quantum theory -- Quantum field theory; related classical field theories -- Anomalies msc Numerical analysis -- Acceleration of convergence -- Euler-Maclaurin formula msc Integral (DE-588)4131477-3 gnd rswk-swf Spur Mathematik (DE-588)4202272-1 gnd rswk-swf Regularisierung (DE-588)4124043-1 gnd rswk-swf Summierbarkeit (DE-588)4294383-8 gnd rswk-swf Regularisierung (DE-588)4124043-1 s Integral (DE-588)4131477-3 s Spur Mathematik (DE-588)4202272-1 s Summierbarkeit (DE-588)4294383-8 s DE-604 Erscheint auch als Online-Ausgabe 978-0-8218-9035-6 University lecture series 59 (DE-604)BV004153846 59 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Paycha, Sylvie 1960- Regularised integrals, sums and traces an analytic point of view University lecture series Quantentheorie Functions, Zeta L-functions Convergence Integrals Number theory -- Zeta and L-functions: analytic theory -- \zeta (s) and L(s, \chi) msc Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of integrals msc Operator theory -- Linear spaces and algebras of operators -- Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) msc Quantum theory -- Quantum field theory; related classical field theories -- Anomalies msc Numerical analysis -- Acceleration of convergence -- Euler-Maclaurin formula msc Integral (DE-588)4131477-3 gnd Spur Mathematik (DE-588)4202272-1 gnd Regularisierung (DE-588)4124043-1 gnd Summierbarkeit (DE-588)4294383-8 gnd |
| subject_GND | (DE-588)4131477-3 (DE-588)4202272-1 (DE-588)4124043-1 (DE-588)4294383-8 |
| title | Regularised integrals, sums and traces an analytic point of view |
| title_auth | Regularised integrals, sums and traces an analytic point of view |
| title_exact_search | Regularised integrals, sums and traces an analytic point of view |
| title_full | Regularised integrals, sums and traces an analytic point of view Sylvie Paycha |
| title_fullStr | Regularised integrals, sums and traces an analytic point of view Sylvie Paycha |
| title_full_unstemmed | Regularised integrals, sums and traces an analytic point of view Sylvie Paycha |
| title_short | Regularised integrals, sums and traces |
| title_sort | regularised integrals sums and traces an analytic point of view |
| title_sub | an analytic point of view |
| topic | Quantentheorie Functions, Zeta L-functions Convergence Integrals Number theory -- Zeta and L-functions: analytic theory -- \zeta (s) and L(s, \chi) msc Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of integrals msc Operator theory -- Linear spaces and algebras of operators -- Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) msc Quantum theory -- Quantum field theory; related classical field theories -- Anomalies msc Numerical analysis -- Acceleration of convergence -- Euler-Maclaurin formula msc Integral (DE-588)4131477-3 gnd Spur Mathematik (DE-588)4202272-1 gnd Regularisierung (DE-588)4124043-1 gnd Summierbarkeit (DE-588)4294383-8 gnd |
| topic_facet | Quantentheorie Functions, Zeta L-functions Convergence Integrals Number theory -- Zeta and L-functions: analytic theory -- \zeta (s) and L(s, \chi) Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of integrals Operator theory -- Linear spaces and algebras of operators -- Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) Quantum theory -- Quantum field theory; related classical field theories -- Anomalies Numerical analysis -- Acceleration of convergence -- Euler-Maclaurin formula Integral Spur Mathematik Regularisierung Summierbarkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
| work_keys_str_mv | AT paychasylvie regularisedintegralssumsandtracesananalyticpointofview |