Loewner's theorem on monotone matrix functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2019]
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
Volume 354 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 459 Seiten |
| ISBN: | 9783030224219 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV046174452 | ||
| 003 | DE-604 | ||
| 005 | 20210531 | ||
| 007 | t | ||
| 008 | 190925s2019 |||| 00||| eng d | ||
| 020 | |a 9783030224219 |c hardcover |9 978-3-030-22421-9 | ||
| 035 | |a (OCoLC)1123081313 | ||
| 035 | |a (DE-599)BVBBV046174452 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-29T |a DE-20 |a DE-188 |a DE-11 |a DE-83 |a DE-19 | ||
| 084 | |a SK 420 |0 (DE-625)143238: |2 rvk | ||
| 084 | |a SK 490 |0 (DE-625)143242: |2 rvk | ||
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 084 | |a 30E05 |2 msc | ||
| 084 | |a 47A56 |2 msc | ||
| 084 | |a 30B40 |2 msc | ||
| 084 | |a 26A48 |2 msc | ||
| 084 | |a 26A51 |2 msc | ||
| 084 | |a 47A63 |2 msc | ||
| 100 | 1 | |a Simon, Barry |d 1946- |e Verfasser |0 (DE-588)134200195 |4 aut | |
| 245 | 1 | 0 | |a Loewner's theorem on monotone matrix functions |c Barry Simon |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a xi, 459 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v Volume 354 | |
| 650 | 0 | 7 | |a Operatortheorie |0 (DE-588)4075665-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrische Funktionentheorie |0 (DE-588)4156711-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 0 | 1 | |a Operatortheorie |0 (DE-588)4075665-8 |D s |
| 689 | 0 | 2 | |a Geometrische Funktionentheorie |0 (DE-588)4156711-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-030-22422-6 |
| 830 | 0 | |a Grundlehren der mathematischen Wissenschaften |v Volume 354 |w (DE-604)BV000000395 |9 354 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031554125&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-031554125 | ||
Datensatz im Suchindex
| _version_ | 1804180535019307008 |
|---|---|
| adam_text | Contents
Parti r‘- :s
1 Imf trtion: The Statement of Loewner’s Theorem 3
2 Some Generalities 11
3 The Herglotz Representation Theorems and the Easy Direction
of Loewner’s Theorem 17
4 Monotonicity of the Square Root 33
5 Loewner Matrices 43
6 Heinävaara’s Integral Formula and the Dobsch-Donoghue Theorem 73
7 M„+1 85
8 Heinävaara’s Second Proof of the Dobsch-Donoghue Theorem 89
9 Convexity, I: The Theorem of Bendat-Kraus-Sherman-Uchiyama 95
10 Convexity, II: Concavity and Monotonicity 107
11 Convexity, III: Hansen-Jensen-Pedersen (HJP) Inequality 117
12 Convexity, IV: Bhatia-Hiai-Sano (BHS) Theorem 123
13 Convexity, V: Strongly Operator Convex Functions 135
14 2x2 Matrices: The Donoghue and Hansen-Tomiyama Theorems 145
15 Quadratic Interpolation: The Foia§-Lions Theorem 153
Part II Proofs of the Hard Direction
16 Pick Interpolation, I: The Basics 165
17 Pick Interpolation, II: Hilbert Space Proof 175
18 Pick Interpolation, III: Continued Fraction Proof 183
ix
Contents
19 Pick Interpolation, IV: Commutant Lifting Proof 189
20 A Proof of Loewner’s Theorem as a Degenerate Limit of Pick’s
Theorem 215
21 Rational Approximation and Orthogonal Polynomials 221
22 Divided Differences and Polynomial Approximation 235
23 Divided Differences and Multipoint Rational Interpolation 247
24 Pick Interpolation, V: Rational Interpolation Proof 263
25 Loewner’s Theorem via Rational Interpolation: Loewner’s Proof_ 267
26 The Moment Problem and the Bendat-Sherman Proof 273
27 Hilbert Space Methods and the Koranyi Proof 283
28 The Krein-Milman Theorem and Hansen’s Variant of the
Hansen-Pedersen Proof 289
29 Positive Functions and Sparr’s Proof 301
30 Ameur’s Proof Using Quadratic Interpolation 313
31 One-Point Continued Fractions: The Wigner-von Neumann Proof 321
32 Multipoint Continued Fractions: A New Proof 333
33 Hardy Spaces and the Rosenblum-Rovnyak Proof 339
34 Mellin Transforms: Boutet de Monvel’s Proof 345
35 Loewner’s Theorem for General Open Sets 359
Part IH Applications and Extensions
36 Operator Means, I: Basics and Examples 373
37 Operator Means, II: Kubo-Ando Theorem 379
38 Lieb Concavity and Lieb-Ruskai Strong Subadditivity
Theorems, I: Basics 385
39 Lieb Concavity and Lieb-Ruskai Strong Subadditivity
Theorems, n: Effros’ Proof 393
40 Lieb Concavity and Lieb-Ruskai Strong Subadditivity
Theorems, III: Ando’s Proof 395
41 Lieb Concavity and Lieb-Ruskai Strong Subadditivity
Theorems, IV: Aujla-Hansen-Uhlmann Proof 397
42 Unitarily Invariant Norms and Rearrangement 399
43 Unitarily Invariant Norm Inequalities 409
Contents X1
A Boutet de Monvel’s Note 415
B Pictures 423
C Symbol List 427
Bibliography 433
Name Index 447
|
| any_adam_object | 1 |
| author | Simon, Barry 1946- |
| author_GND | (DE-588)134200195 |
| author_facet | Simon, Barry 1946- |
| author_role | aut |
| author_sort | Simon, Barry 1946- |
| author_variant | b s bs |
| building | Verbundindex |
| bvnumber | BV046174452 |
| classification_rvk | SK 420 SK 490 SK 620 |
| ctrlnum | (OCoLC)1123081313 (DE-599)BVBBV046174452 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01995nam a2200505 cb4500</leader><controlfield tag="001">BV046174452</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210531 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">190925s2019 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783030224219</subfield><subfield code="c">hardcover</subfield><subfield code="9">978-3-030-22421-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1123081313</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV046174452</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 420</subfield><subfield code="0">(DE-625)143238:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 490</subfield><subfield code="0">(DE-625)143242:</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">30E05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47A56</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">30B40</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">26A48</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">26A51</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47A63</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Simon, Barry</subfield><subfield code="d">1946-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)134200195</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Loewner's theorem on monotone matrix functions</subfield><subfield code="c">Barry Simon</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham, Switzerland</subfield><subfield code="b">Springer</subfield><subfield code="c">[2019]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2019</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xi, 459 Seiten</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">Grundlehren der mathematischen Wissenschaften</subfield><subfield code="v">Volume 354</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Operatortheorie</subfield><subfield code="0">(DE-588)4075665-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrische Funktionentheorie</subfield><subfield code="0">(DE-588)4156711-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Operatortheorie</subfield><subfield code="0">(DE-588)4075665-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Geometrische Funktionentheorie</subfield><subfield code="0">(DE-588)4156711-0</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">978-3-030-22422-6</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Grundlehren der mathematischen Wissenschaften</subfield><subfield code="v">Volume 354</subfield><subfield code="w">(DE-604)BV000000395</subfield><subfield code="9">354</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS 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=031554125&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:BVB01-031554125</subfield></datafield></record></collection> |
| id | DE-604.BV046174452 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:37:18Z |
| institution | BVB |
| isbn | 9783030224219 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031554125 |
| oclc_num | 1123081313 |
| open_access_boolean | |
| owner | DE-29T DE-20 DE-188 DE-11 DE-83 DE-19 DE-BY-UBM |
| owner_facet | DE-29T DE-20 DE-188 DE-11 DE-83 DE-19 DE-BY-UBM |
| physical | xi, 459 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Simon, Barry 1946- Verfasser (DE-588)134200195 aut Loewner's theorem on monotone matrix functions Barry Simon Cham, Switzerland Springer [2019] © 2019 xi, 459 Seiten txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften Volume 354 Operatortheorie (DE-588)4075665-8 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s Operatortheorie (DE-588)4075665-8 s Geometrische Funktionentheorie (DE-588)4156711-0 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-22422-6 Grundlehren der mathematischen Wissenschaften Volume 354 (DE-604)BV000000395 354 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031554125&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simon, Barry 1946- Loewner's theorem on monotone matrix functions Grundlehren der mathematischen Wissenschaften Operatortheorie (DE-588)4075665-8 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4156711-0 (DE-588)4001865-9 |
| title | Loewner's theorem on monotone matrix functions |
| title_auth | Loewner's theorem on monotone matrix functions |
| title_exact_search | Loewner's theorem on monotone matrix functions |
| title_full | Loewner's theorem on monotone matrix functions Barry Simon |
| title_fullStr | Loewner's theorem on monotone matrix functions Barry Simon |
| title_full_unstemmed | Loewner's theorem on monotone matrix functions Barry Simon |
| title_short | Loewner's theorem on monotone matrix functions |
| title_sort | loewner s theorem on monotone matrix functions |
| topic | Operatortheorie (DE-588)4075665-8 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Operatortheorie Geometrische Funktionentheorie Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031554125&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT simonbarry loewnerstheoremonmonotonematrixfunctions |