Bitangential direct and inverse problems for systems of integral and differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
145 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | XIV, 472 S. |
| ISBN: | 9781107018877 |
Internformat
MARC
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| 100 | 1 | |a Arov, Damir Z. |d 1934- |e Verfasser |0 (DE-588)172974356 |4 aut | |
| 245 | 1 | 0 | |a Bitangential direct and inverse problems for systems of integral and differential equations |c Damir Z. Arov ; Harry Dym |
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2012 | |
| 300 | |a XIV, 472 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 145 | |
| 500 | |a Includes bibliographical references | ||
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integralgleichung |0 (DE-588)4027229-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a System von partiellen Differentialgleichungen |0 (DE-588)4116672-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a System von partiellen Differentialgleichungen |0 (DE-588)4116672-3 |D s |
| 689 | 0 | 1 | |a Integralgleichung |0 (DE-588)4027229-1 |D s |
| 689 | 0 | 2 | |a Inverses Problem |0 (DE-588)4125161-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Dym, Harry |d 1938- |e Verfasser |0 (DE-588)124041205 |4 aut | |
| 830 | 0 | |a Encyclopedia of mathematics and its applications |v 145 |w (DE-604)BV000903719 |9 145 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025903623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025903623 | ||
Datensatz im Suchindex
| _version_ | 1804150220883230720 |
|---|---|
| adam_text | CONTENTS
Preface page
xiii
1
Introduction
1
1.1
The matrizant as a chain of entire
У
-inner
mvf s
2
1.2
Monodromy matrices of regular systems
4
1.3
Canonical integral systems
5
1.4
Singular, right regular and right strongly regular matrizants
6
1.5
Input scattering matrices
8
1.6
Chains of associated pairs of the first kind
9
1.7
The bitangential direct input scattering problem
11
1.8
Bitangential inverse monodromy and inverse
scattering problems
12
1.9
The generalized
Schur
interpolation problem
13
1.10
Identifying matrizants as resolvent matrices when
/ =
jpq
14
1.11
Input impedance matrices and spectral functions
15
1.12 de
Branges spaces
17
1.13
Bitangential direct and inverse input impedance and
spectral problems
19
1.14
Krein exten sion problems and Dirac systems
21
1.15
Direct and inverse problems for Dirac-Krein systems
23
1.16
Supplementary notes
25
2
Canonical systems and related differential equations
27
2.1
Canonical integral systems
27
2.2
Connections with canonical differential systems
30
2.3
The matrizant and its properties
33
2.4
Regular case: Monodromy matrix
36
viii Contents
2.5
Multiplicative integral
formulas
for matrizants and
monodramy
matrices; Potapov s theorems
37
2.6
The Feller-Krein string equation
43
2.7
Differential systems with potential
47
2.8
Dirac-Krein systems
49
2.9
The
Schrödinger
equation
51
2.10
Supplementary notes
53
3
Matrix-valued functions in the Nevanlinna class
56
3.1
Preliminaries on the Nevanlinna class
Λίρχ<ι
58
3.2
Linear fractional transformations and Redheffer
transformations
65
3.3
The Riesz-Herglotz-Nevanlinna representation
69
3.4
The class
£
П
Ν1 *4
of entire mvf s in
ЛЛ1*«
74
3.5
The class
ΓΡΧί
of mvf s in Krpxq with pseudocontinuatkms
77
3.6
Fourier transforms and Paley-Wiener theorems
79
3.7
Entire inner mvf s
81
3.8 /
contractive, /-inner and entire /-inner mvf s
84
3.9
Associated pairs of the first kind
91
3.10
Singular and right (and left) regular /-inner mvf s
93
3.11
Linear fractional transformations of SpXi into itself
96
3.12
Linear fractional transformations in Cpxp and from Spxp
into
C
98
3.13
Associated pairs of the second kind
102
3.14
Supplementary notes
105
4
Interpolation problems, resolvent matrices and
de Branges
spaces
107
4.1
The Nehari problem
108
4.2
The generalized
Schur
interpolation problem
112
4.3
Right and left strongly regular /-inner mvf s
118
4.4
The generalized
Carathéodory
interpolation problem
119
4.5
Detour on scalar determinate interpolation problems
124
4.6
The reproducing kernel Hubert space %{U)
127
4.7
de
Branges inclusion theorems
135
4.8
A description of H(W)
Π
Щ
137
4.9
The classes UAr
(7)
and
Um
(/)
of
л
-regular and
Ä-regular
/-inner mvf
s
140
4.10
de
Branges matrices
(S
and
de
Branges spaces B((£)
143
4.11
A coisometry from H(A) onto
B(ß) 148
4.12
Formulas for resolvent matrices
W
є
£
Π
U°sR
(јрч
) 149
4.13
Formulas for resolvent matrices
А є Є
Π
U^R (Jp)
151
4.14
Supplementary notes
155
Contents ix
5
Chains that are matrizants and chains of associated pairs
158
5.1
Continuous chains of entire /-inner mvf s
158
5.2
Chains that are matrizants
162
5.3
Continuity of chains of associated pairs
167
5.4
Type functions for chains
170
5.5
Supplementary notes
177
6
The bitangential direct input scattering problem
178
6.1
The set
<S¿.lt(<iM)
of input scattering matrices
178
6.2
Parametrization of Sfcat(dM) in terms of
Redheffer transforms
181
6.3
Regular canonical integral systems
183
6.4
Limit balls for input scattering matrices
184
6.5
The full rank case
189
6.6
Rank formulas
192
6.7
Regular systems
(=
full rank) case
193
6.8
The limit point case
193
6.9
The diagonal case
195
6.10
A Weyl-Titchmarsh like characterization for input
scattering matrices
195
6.11
Supplementary notes
200
7
Bitangential direct input impedance and spectral problems
202
7.
1 Input impedance matrices
202
7.2
Limit balls for input impedance matrices
206
7.3
Formulas for the ranks of semiradii of the limit ball
209
7.4
Bounded mass functions and full rank end points
211
7.5
The limit point case
213
7.6
The Weyl-Titchmarsh characterization of the input
impedance
215
7.7
Spectral functions for canonical systems
219
7.8
Parametrization of the set (H(A))psf
225
7.9
Parametrization of the set
Σ ^.
(dM) for regular canonical
integral systems
230
7.10
Pseudospectral and spectral functions for singular systems
232
7.11
Supplementary notes
237
8
Inverse
monodramy
problems
241
8.1
Some simple illustrative examples
244
8.2
Extremal solutions when
J
=
lm
247
8.3
Solutions for
U
є
UAR(J) when
J
φ
±Im
253
8.4
Connections with the Livsic model of
a Volteira
node
258
8.5
Conditions for the uniqueness of normalized Hamiltonians
269
χ
Contents
8.6 Solutions
with symplectic and/or real matrizants
277
8.7
Entire homogeneous resolvent matrices
281
8.8
Solutions with homogeneous matrizants
285
8.9
Extremal solutions for
J
φ
±Im
291
8.10
The unicellular case for
J
φ
±Im
294
8.11
Solutions with symmetric type
295
8.12
The inverse
monodramy
problem for
2x2
differential systems
299
8.13
Examples of
2
χ
2
Hamiltonians with constant determinant
304
8.14
Supplementary notes
308
9
Bitangential Krein extension problems
310
9.1
Helical extension problems
311
9.2
Bitangential helical extension problems
317
9.3
The Krein accelerant extension problem
320
9.4
Continuous analogs of the
Schur
extension problem
328
9.5
A bitangential generalization of the
Schur
extension problem
334
9.6
The Nehari extension problem for mvf s in Wiener class
338
9.7
Continuous analogs of the
Schur
extension problem for mvf s
in the Wiener class
347
9.8
Bitangential
Schur
extension problems in the Wiener class
350
9.9
Supplementary notes
354
10
Bitangential inverse input scattering problems
355
10.1
Existence and uniqueness of solutions
356
10.2
Formulas for the solution of the inverse input
scattering problem
357
10.3
Input scattering matrices in the Wiener class
361
10.4
Examples with diagonal mvf s
Ух
and
Ы,
362
10.5
Supplementary notes
371
11
Bitangential inverse input impedance and spectral problems
372
11.1
Existence and uniqueness of solutions
373
11.2
Formulas for the solutions
375
11.3
Input impedance matrices in the Wiener class
378
11.4
Examples with diagonal mvf s tf3 and tf4 = IP
383
11.5
The bitangential inverse spectral problem
393
11.6
An example
396
11.7
Supplementary notes
406
12
Direct and inverse problems for Dirac-Krein systems
409
12.1
Factoring Hamiltonians corresponding to DK-systems
411
12.2
Matrizants of canonical differential systems corresponding to
DK-systems
416
Contents xi
12.3
Direct
and inverse raonodromy problems for DK-systems
423
12.4
Direct and inverse input scattering problems for DK-systems
424
12.5
Direct and inverse input impedance problems for DK-systems
427
12.6
Direct and inverse spectral problems for DK-systems
431
12.7
The Krein algorithms for the inverse input scattering and
impedance problems
433
12.8
The left transform
Г^
for 2lf
є
WfUw)
435
12.9
Asymptotic equivalence matrices
438
12.10
Asymptotic scattering matrices (S-marrices)
438
12.11
The inverse asymptotic scattering problem
443
12.12
More on spectral functions of DK-systems
445
12.13
Supplementary notes
447
References
450
Symbol index
465
Index
469
|
| any_adam_object | 1 |
| author | Arov, Damir Z. 1934- Dym, Harry 1938- |
| author_GND | (DE-588)172974356 (DE-588)124041205 |
| author_facet | Arov, Damir Z. 1934- Dym, Harry 1938- |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)844045628 (DE-599)BVBBV040924535 |
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| id | DE-604.BV040924535 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:35:28Z |
| institution | BVB |
| isbn | 9781107018877 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025903623 |
| oclc_num | 844045628 |
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| owner_facet | DE-355 DE-BY-UBR |
| physical | XIV, 472 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Arov, Damir Z. 1934- Verfasser (DE-588)172974356 aut Bitangential direct and inverse problems for systems of integral and differential equations Damir Z. Arov ; Harry Dym Cambridge [u.a.] Cambridge Univ. Press 2012 XIV, 472 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 145 Includes bibliographical references Inverses Problem (DE-588)4125161-1 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd rswk-swf System von partiellen Differentialgleichungen (DE-588)4116672-3 s Integralgleichung (DE-588)4027229-1 s Inverses Problem (DE-588)4125161-1 s DE-604 Dym, Harry 1938- Verfasser (DE-588)124041205 aut Encyclopedia of mathematics and its applications 145 (DE-604)BV000903719 145 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025903623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arov, Damir Z. 1934- Dym, Harry 1938- Bitangential direct and inverse problems for systems of integral and differential equations Encyclopedia of mathematics and its applications Inverses Problem (DE-588)4125161-1 gnd Integralgleichung (DE-588)4027229-1 gnd System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4027229-1 (DE-588)4116672-3 |
| title | Bitangential direct and inverse problems for systems of integral and differential equations |
| title_auth | Bitangential direct and inverse problems for systems of integral and differential equations |
| title_exact_search | Bitangential direct and inverse problems for systems of integral and differential equations |
| title_full | Bitangential direct and inverse problems for systems of integral and differential equations Damir Z. Arov ; Harry Dym |
| title_fullStr | Bitangential direct and inverse problems for systems of integral and differential equations Damir Z. Arov ; Harry Dym |
| title_full_unstemmed | Bitangential direct and inverse problems for systems of integral and differential equations Damir Z. Arov ; Harry Dym |
| title_short | Bitangential direct and inverse problems for systems of integral and differential equations |
| title_sort | bitangential direct and inverse problems for systems of integral and differential equations |
| topic | Inverses Problem (DE-588)4125161-1 gnd Integralgleichung (DE-588)4027229-1 gnd System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd |
| topic_facet | Inverses Problem Integralgleichung System von partiellen Differentialgleichungen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025903623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
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