Completeness of root functions of regular differential operators:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman Scientific & Technical
1994
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
71 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 245 S. |
| ISBN: | 0582236924 |
Staff View
MARC
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| 100 | 1 | |a Yakubov, Sasun |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Completeness of root functions of regular differential operators |c Sasun Yakubov |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman Scientific & Technical |c 1994 | |
| 300 | |a 245 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman monographs and surveys in pure and applied mathematics |v 71 | |
| 650 | 4 | |a Differentialoperator - Vollständigkeit | |
| 650 | 4 | |a Partielle Differentialgleichung - Numerisches Verfahren - Polynomoperator | |
| 650 | 4 | |a Randwertproblem - Numerisches Verfahren - Unbeschränkter Operator | |
| 650 | 0 | 7 | |a Differentialoperator |0 (DE-588)4012251-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialoperator |0 (DE-588)4012251-7 |D s |
| 689 | 0 | 1 | |a Funktionentheorie |0 (DE-588)4018935-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Pitman monographs and surveys in pure and applied mathematics |v 71 |w (DE-604)BV000022446 |9 71 | |
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Record in the Search Index
| _version_ | 1804124311899865088 |
|---|---|
| adam_text | CONTENTS
Introduction 1
Chapter 1. Auxiliary results 7
1.1. General notions from functional analysis 7
1.1.1. Linear spaces 7
1.1.2. Banach spaces 8
1.1.3. Operators in Banach spaces 8
1.1.4. Dual spaces 10
1.1.5. Adjoint operators 11
1.1.6. Hilbert spaces 11
1.1.7. Continuity of a vector valued function 12
1.1.8. Differentiable and analytic vector valued functions 12
1.1.9. Measurability of a vector valued function 13
1.1.10. Bochner integral 13
1.1.11. Generalized derivative of a vector valued function 14
1.1.12. Functional spaces of vector valued functions 14
1.1.13. Fourier multipliers 15
1.2. Interpolation of spaces and operators 15
1.2.1. Embedding of spaces 15
1.2.2. Embedding of dual spaces 16
1.2.3. Interpolation spaces 17
1.2.4. Sobolev spaces and their interpolation 19
1.2.5. Operators in interpolation spaces 21
1.2.6. Inequalities 21
Chapter 2. Unbounded polynomial operator pencils 23
2.0. Introduction 23
2.1. Completeness of root vectors of an operator from the class
rP(H) 24
2.1.1. Notations and definitions 24
2.1.2. Invariant subspaces and restrictions of an operator;
Projectors; Orthogonal projectors 27
2.1.3. Laurent series expansion of the resolvent 28
2.1.4. Infinite products 30
2.1.5. The Phragmen Lindelof principle 31
2.1.6. Polar representation of a bounded operator 33
2.1.7. s numbers of a compact operator 33
2.1.8. Schmidt expansion for a compact operator 34
2.1.9. Elementary properties of s numbers 34
2.1.10. Weyl s inequality:a correlation between the eigenval¬
ues and the s numbers 35
2.1.11. Classes ap(H,Hx) 36
CONTENTS
2.1.12. A growth estimate for the resolvent of a Volterra op¬
erator from the class crp(H) 38
2.1.13. Completeness of root vectors of an operator from the
class ap(H) 40
2.2. Completeness of root vectors of an unbounded operator 46
2.2.1. Completeness of root vectors of an operator with a
compact resolvent 47
2.2.2. Expansion of a smooth vector in the root subspaces
of an unbounded operator 49
2.2.3. Completeness of root vectors of an operator with the
resolvent from the class crp(H) 50
2.2.4. Comparison of operators 52
2.2.5. Perturbation of an operator with a decreasing resol¬
vent 54
2.2.6. Completeness of root vectors of a perturbed un¬
bounded operator 55
2.2.7. Completeness of root vectors of a perturbed un¬
bounded selfadjoint operator 56
2.2.8. Expansion of a smooth vector in the root subspaces
of the perturbed unbounded operator 57
2.2.9. Expansion of a smooth vector in the root subspaces
of the perturbed unbounded selfadjoint operator 58
2.3. n fold completeness of root vectors of a system of unbounded
polynomial operator pencils 60
2.3.1. A system of unbounded polynomial operator pencils 60
2.3.2. A system of operator pencils that are partially poly
nomially dependent on the parameter 69
2.3.3. n fold completeness of root vectors of a perturbed
coercive operator pencil with a defect 71
2.3.4. n fold completeness of root vectors of an operator
pencil with a weight 75
2.3.5. n fold completeness of root vectors for the Keldysh
operator pencil 77
2.3.6. (u(0), u (0)) completeness of root vectors, corre¬
sponding to a part of the operator pencil spectrum
79
2.4. Completeness of root vectors of a system of unbounded linear
operator pencils 82
Chapter 3. Principally boundary value problems for or¬
dinary differential equations with a polynomial pa¬
rameter 86
3.0. Introduction 86
3.0.1. p regular functional conditions 87
CONTENTS
3.1. Coerciveness of principally boundary value problems for or¬
dinary differential equations with a polynomial parameter 88
3.1.1. Coerciveness of the principal part of a boundary value
problem for equations with constant coefficients 88
3.1.2. Fredholm property of the problem with general func¬
tional conditions 96
3.1.3. Coerciveness of the problem for equations with con¬
stant coefficients 97
3.1.4. Coerciveness of the problem for equations with vari¬
able coefficients 98
3.2. Fold completeness of root functions of principally bound¬
ary value problems for ordinary differential equations with
a polynomial parameter 109
3.2.1. Dense sets in spaces of Sobolev type 111
3.2.2. n fold completeness of root functions 115
3.3. Completeness of root functions of principally boundary value
problems for ordinary differential equations with a linear pa¬
rameter 122
Chapter 4. Principally elliptic boundary value problem
with a polynomial parameter 129
4.0. Introduction 129
4.1. Principally regular elliptic boundary value problems with a
polynomial parameter 132
4.1.1. Coerciveness of principally regular elliptic boundary
value problems 135
4.1.2. Dense sets in Sobolev spaces 140
4.1.3. Fold completeness of root functions of principally reg¬
ular elliptic boundary value problems 144
4.2. Irregular elliptic boundary value problems for the Laplace
equation 151
4.2.1. A boundary value problem for the Laplace equation
with non classical spectral asymptotics 151
4.2.2. Non coerciveness of the boundary value problem 153
4.2.3. A boundary value problem for the Laplace equation
with an infinite dimensional kernel 156
Chapter 5. Differential operator equations 160
5.1. Differential operator equations on the whole axis 160
5.1.1. Compactriess of embeddings 160
5.1.2. Coercive equations of the higher order 163
5.2. The Cauchy problem for parabolic differential operator equa¬
tions 170
CONTENTS
5.2.1. Homogeneous equations with a constant operator in
a Banach space 170
5.2.2. Nonhomogeneous equations with a constant operator
in a Banach space 176
5.2.3. Nonhomogeneous equations with a variable operator
in a Hilbert space 181
5.3. Boundary value problems for elliptic differential operator
equations 185
5.3.1. Fredholm property of a boundary value problem for
elliptic differential operator equations on [0,1] 185
5.3.2. An isomorphism generated by a boundary value prob¬
lem for elliptic differential operator equations on a
semi axis 194
5.4. Completeness of elementary solutions of differential operator
equations 200
5.4.1. Completeness of elementary solutions of parabolic
differential operator equations 200
5.4.2. Completeness of elementary solutions for elliptic dif¬
ferential operator equations 203
Chapter 6. Partial differential equations 206
6.1. Principally initial boundary value problems for parabolic
equations 206
6.1.1. An isomorphism of principally initial boundary value
problems for parabolic equations 206
6.1.2. Completeness of elementary solutions of principally
initial boundary value problems for parabolic equa¬
tions 210
6.2. Boundary value problems for elliptic equations of the 4 th
order 213
6.2.1. Fredholm property of boundary value problems for
elliptic equations 213
6.2.2. An isomorphism of boundary value problems for el¬
liptic equations 220
6.2.3. Completeness of elementary solutions of boundary
value problems for elliptic equations 223
Reference notes 229
References 234
List of notations 240
Subject index 241
Author index 243
|
| any_adam_object | 1 |
| author | Yakubov, Sasun |
| author_facet | Yakubov, Sasun |
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| id | DE-604.BV009943064 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:43:39Z |
| institution | BVB |
| isbn | 0582236924 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006588160 |
| oclc_num | 246503646 |
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| owner_facet | DE-91G DE-BY-TUM DE-824 DE-634 DE-11 DE-188 |
| physical | 245 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Longman Scientific & Technical |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Yakubov, Sasun Verfasser aut Completeness of root functions of regular differential operators Sasun Yakubov 1. publ. Harlow, Essex Longman Scientific & Technical 1994 245 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 71 Differentialoperator - Vollständigkeit Partielle Differentialgleichung - Numerisches Verfahren - Polynomoperator Randwertproblem - Numerisches Verfahren - Unbeschränkter Operator Differentialoperator (DE-588)4012251-7 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Differentialoperator (DE-588)4012251-7 s Funktionentheorie (DE-588)4018935-1 s DE-604 Pitman monographs and surveys in pure and applied mathematics 71 (DE-604)BV000022446 71 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006588160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yakubov, Sasun Completeness of root functions of regular differential operators Pitman monographs and surveys in pure and applied mathematics Differentialoperator - Vollständigkeit Partielle Differentialgleichung - Numerisches Verfahren - Polynomoperator Randwertproblem - Numerisches Verfahren - Unbeschränkter Operator Differentialoperator (DE-588)4012251-7 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4012251-7 (DE-588)4018935-1 |
| title | Completeness of root functions of regular differential operators |
| title_auth | Completeness of root functions of regular differential operators |
| title_exact_search | Completeness of root functions of regular differential operators |
| title_full | Completeness of root functions of regular differential operators Sasun Yakubov |
| title_fullStr | Completeness of root functions of regular differential operators Sasun Yakubov |
| title_full_unstemmed | Completeness of root functions of regular differential operators Sasun Yakubov |
| title_short | Completeness of root functions of regular differential operators |
| title_sort | completeness of root functions of regular differential operators |
| topic | Differentialoperator - Vollständigkeit Partielle Differentialgleichung - Numerisches Verfahren - Polynomoperator Randwertproblem - Numerisches Verfahren - Unbeschränkter Operator Differentialoperator (DE-588)4012251-7 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Differentialoperator - Vollständigkeit Partielle Differentialgleichung - Numerisches Verfahren - Polynomoperator Randwertproblem - Numerisches Verfahren - Unbeschränkter Operator Differentialoperator Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006588160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
| work_keys_str_mv | AT yakubovsasun completenessofrootfunctionsofregulardifferentialoperators |