Regularity of difference equations on Banach spaces:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2014
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XV, 208 S. |
| ISBN: | 9783319064468 |
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MARC
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| 245 | 1 | 0 | |a Regularity of difference equations on Banach spaces |c Ravi P. Agarwal ; Claudio Cuevas ; Carlos Lizama |
| 264 | 1 | |a Cham [u.a.] |b Springer |c 2014 | |
| 300 | |a XV, 208 S. | ||
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Record in the Search Index
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Contents
1
Discrete
Semigroups and Cosine Operators
. 1
1.
ł
Difference Equations on Banach Spaces
. 2
1.2
The Transform Method
. 3
1
.3
Discrete Semigroups Operators
. 7
1.4
Discrete Cosine and Sine Operators
. 11
1.5
Comments
. 15
2
Maximal Regularity and the Method of Fourier Multipliers
. 19
2.1
UM D
Spaces
. 20
2.2 Ä-Boundedness. 21
2.3
Maximal
Ľ7
-Regularity
. 27
2.4
Vector-Valued Fourier Multipliers: Blunck's Theorem
. 30
2.5
Comments
. 34
3
First-Order Linear Difference Equations
. 47
3.1
A Characterization of Maximal /^-Regularity
. 47
3.2
Maximal /^-Regularity for
p
є
{1
,
2.
oo}
. 51
3.3
Comments
. 54
4
First-Order Semilinear Difference Equations
. 57
4.1
Existence for the Semilinear Problem
. 57
4.2
Local Perturbations
. 65
4.3
Comments
. 69
5
Second-Order Linear Difference Equations
. 71
5.1
Discrete Maximal Regularity
. 71
5.2
Exact Discretizations
. 74
5.3
Exact Second-Order Difference Equation
. 77
5.4
a Characterization of Maximal lp-Regularity
. 79
5.5
Regularity in Weighted lp Spaces
. 82
5.6
Well-Posedness and the
Maximai
Regularity Space
. 89
5.7
Comments
. 91
IX
x
Contents
6
Second-Order
Semilinear
Difference Equations
. 99
6.1 Semilinear
Second-Order Equations
. 99
6.2
Exact Semilinear Second-Order Equations
. 101
6.3
Semilinear Problems on Weighted Spaces
. 108
6.4
Local Perturbations
.
Ill
6.5
Local Perturbations for the Harmonic Oscillator
. 112
6.6
Local Perturbations on Weighted Spaces
. 116
6.7
Comments
. 118
7
Applications
. 119
7.
1
Semilinear Difference Equations
. 119
7.2
An Arendt-Duelli-Type Theorem
. 123
7.3
An
Ä-Boundedness
Criterion
. 130
7.4
Stability
. 134
7.5
Boundedness
. 141
7.6
Asymptotic Behavior
. 153
7.7
Boundedness for RFDE via Maximal Regularity
. 161
7.8
More About Boundedness and Asymptotic Behavior for RFDE
_ 180
7.9
Volteira
Difference System with Infinite Delay
. 188
7.10
Comments
. 195
References
. 199
Index
. 207
Ravi P. Agarwal
·
Claudio
Cuevas
·
Carlos
Uzama
Regularity of Difference Equations on Banach Spaces
This work introduces readers to the topic of maximal regularity for difference equations.
The authors systematically present the method of maximal regularity, outlining basic
linear difference equations along with relevant results. They address recent advances
in the field, as well as basic semigroup and cosine operator theories in the discrete
setting. The authors also identify some open problems that readers may wish to take
up for further research. This book is intended for graduate students and researchers
in the area of difference equations, particularly those with advance knowledge of and
interest in functional analysis. |
| any_adam_object | 1 |
| author | Agarwal, Ravi P. 1947- Cuevas, Claudio Lizama, Carlos 1961- |
| author_GND | (DE-588)112040187 (DE-588)105430064X (DE-588)1054300879 |
| author_facet | Agarwal, Ravi P. 1947- Cuevas, Claudio Lizama, Carlos 1961- |
| author_role | aut aut aut |
| author_sort | Agarwal, Ravi P. 1947- |
| author_variant | r p a rp rpa c c cc c l cl |
| building | Verbundindex |
| bvnumber | BV042029922 |
| classification_rvk | SK 580 |
| ctrlnum | (OCoLC)891295945 (DE-599)BVBBV042029922 |
| dewey-full | 515.625 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.625 |
| dewey-search | 515.625 |
| dewey-sort | 3515.625 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042029922 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-02T15:00:34Z |
| institution | BVB |
| isbn | 9783319064468 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027471388 |
| oclc_num | 891295945 |
| open_access_boolean | |
| owner | DE-11 DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-11 DE-355 DE-BY-UBR DE-188 |
| physical | XV, 208 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| spelling | Agarwal, Ravi P. 1947- Verfasser (DE-588)112040187 aut Regularity of difference equations on Banach spaces Ravi P. Agarwal ; Claudio Cuevas ; Carlos Lizama Cham [u.a.] Springer 2014 XV, 208 S. txt rdacontent n rdamedia nc rdacarrier Banach-Raum (DE-588)4004402-6 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Regularität (DE-588)4049074-9 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 s Banach-Raum (DE-588)4004402-6 s Regularität (DE-588)4049074-9 s DE-604 Cuevas, Claudio Verfasser (DE-588)105430064X aut Lizama, Carlos 1961- Verfasser (DE-588)1054300879 aut Erscheint auch als Online-Ausgabe 978-3-319-06447-5 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027471388&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027471388&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Agarwal, Ravi P. 1947- Cuevas, Claudio Lizama, Carlos 1961- Regularity of difference equations on Banach spaces Banach-Raum (DE-588)4004402-6 gnd Differenzengleichung (DE-588)4012264-5 gnd Regularität (DE-588)4049074-9 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4012264-5 (DE-588)4049074-9 |
| title | Regularity of difference equations on Banach spaces |
| title_auth | Regularity of difference equations on Banach spaces |
| title_exact_search | Regularity of difference equations on Banach spaces |
| title_full | Regularity of difference equations on Banach spaces Ravi P. Agarwal ; Claudio Cuevas ; Carlos Lizama |
| title_fullStr | Regularity of difference equations on Banach spaces Ravi P. Agarwal ; Claudio Cuevas ; Carlos Lizama |
| title_full_unstemmed | Regularity of difference equations on Banach spaces Ravi P. Agarwal ; Claudio Cuevas ; Carlos Lizama |
| title_short | Regularity of difference equations on Banach spaces |
| title_sort | regularity of difference equations on banach spaces |
| topic | Banach-Raum (DE-588)4004402-6 gnd Differenzengleichung (DE-588)4012264-5 gnd Regularität (DE-588)4049074-9 gnd |
| topic_facet | Banach-Raum Differenzengleichung Regularität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027471388&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027471388&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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