Formal analysis: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2021]
|
| Series: | De Gruyter studies in mathematics
volume 80 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 323 Seiten 24 cm x 17 cm |
| ISBN: | 9783110597851 3110597853 |
Staff View
MARC
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| 245 | 1 | 0 | |a Formal analysis |b an introduction |c Xiao-Xiong Gan |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2021] | |
| 264 | 4 | |c © 2021 | |
| 300 | |a XII, 323 Seiten |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804182735964602368 |
|---|---|
| adam_text | CONTENTS
PREFACE
-
VII
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
BASICS
OF
FORMAL
POWER
SERIES
-
1
BASIC
ALGEBRAIC
OPERATIONS
----
2
COMPOSITION
OF
FORMAL
POWER
SERIES
WITH
NONUNIT
----
7
RIGHT
DISTRIBUTIVE
LAW
FOR
COMPOSITION
----
13
THE
MATRIX
REPRESENTATION
OF
FORMAL
POWER
SERIES
-
17
ALMOST
UNIT
FORMAL
POWER
SERIES
-
22
ALGEBRAIC
STRUCTURE
OF
X
-
35
ANALYTIC
STRUCTURE
OF
X
-----38
2
2.1
2.2
2.3
2.4
2.5
CALCULUS
OF
FORMAL
POWER
SERIES
-
49
FORMAL
DERIVATIVES
OF
FORMAL
POWER
SERIES
-
49
FORMAL
DIFFERENTIAL
EQUATIONS
AND
THEIR
APPLICATIONS
-
54
ULTRAMETRIC
-
65
SOME
TOPOLOGICAL
STRUCTURE
FOR
X
----
69
THE
UMBRAL
CALCULUS
AND
FORMAL
POWER
SERIES
-
78
3
3.1
3.2
3.3
3.4
APPLICATIONS
OF
FORMAL
POWER
SERIES,
1
-
85
RIORDAN
GROUP
AND
FORMAL
POWER
SERIES
----
85
RIORDAN
INVOLUTIONS
----
92
SOME
SUBGROUPS
OF
THE
RIORDAN
GROUP
----
93
CAYLEY-HAMILTON
THEOREM
AND
FERMAT
S
LITTLE
THEOREM
-
96
4
4.1
4.2
4.3
4.4
APPLICATIONS
OF
FORMAL
POWER
SERIES,
II
-
101
FORMAL
POWER
SERIES
AND
SOME
DIFFERENTIAL
EQUATIONS
-
101
FUNCTIONAL
EQUATIONS
AND
FORMAL
POWER
SERIES
-
105
LAGRANGE
INVERSION
-
115
DIFFERENCE
EQUATIONS
AND
FORMAL
POWER
SERIES
-
123
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
GENERAL
COMPOSITION
-
129
INTRODUCTION
----
129
MATRIX
REPRESENTATION
OF
THE
GENERAL
COMPOSITION,
1
-
132
COEFFICIENTS
OF
F
N
(Z)
----
135
THE
GENERAL
COMPOSITION
THEOREM
-
141
THE
GENERAL
CHAIN
RULE
----
150
THE
GENERAL
RIGHT
DISTRIBUTIVE
LAW
-
154
MATRIX
REPRESENTATION
OF
THE
GENERAL
COMPOSITION,
II
-
156
XII
-
CONTENTS
BIBLIOGRAPHY
-
315
6
6.1
6.2
6.3
6.4
FORMAL
ANALYSIS
AND
CLASSICAL
ANALYSIS
-
161
INTRODUCTION
TO
THE
BOUNDARY
BEHAVIOR
----
161
BOUNDARY
BEHAVIOR
AND
FORMAL
ANALYSIS
----
166
BANACH
SPACES
H
P
(P)
AND
P
(P)
----
173
GENERAL
FORMAL
LOGARITHM
-
179
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
FORMAL
LAURENT
SERIES
-
189
SEMIFORMAL
LAURENT
SERIES
----
190
REVERSED
SEMIFORMAL
LAURENT
SERIES
-
199
BASIC
ALGEBRA
OF
FORMAL
LAURENT
SERIES
-
206
COMPOSITION
OF
FORMAL
LAURENT
SERIES
AND
FORMAL
POWER
SERIES
-
217
CANONICAL
MAPPING
AND
DOT
PRODUCT
OF
FORMAL
LAURENT
SERIES
-
224
CANONICAL
MAPPING
AND
MULTIPLICATION
OF
FORMAL
LAURENT
SERIES
-
226
TOPOLOGICAL
SPACES
OF
FORMAL
LAURENT
SERIES
-
233
8
8.1
8.2
8.3
8.4
ITERATION
AND
ITERATIVE
ROOTS
-
245
CONJUGACY
OF
FORMAL
POWER
SERIES
IN
D
----
245
THE
ITERATION
OF
FORMAL
POWER
SERIES
----
264
THE
ITERATIVE
ROOTS
OF
FORMAL
SERIES
IN
D
-
269
SCHRODER
S
PROBLEM
-
273
9
9.1
9.2
9.3
9.4
FORMAL
SERIES
AND
GENERAL
EXPONENTS
-
285
INTRODUCTION
----
286
FORMAL
ROOT
SERIES
AND
ITS
ALGORITHM
-
287
POWER
OF
FORMAL
POWER
SERIES
WITH
RATIONAL
EXPONENTS
-
298
THE
REAL
EXPONENTS
OF
FORMAL
POWER
SERIES
-
304
INDEX
-
319
|
| adam_txt |
CONTENTS
PREFACE
-
VII
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
BASICS
OF
FORMAL
POWER
SERIES
-
1
BASIC
ALGEBRAIC
OPERATIONS
----
2
COMPOSITION
OF
FORMAL
POWER
SERIES
WITH
NONUNIT
----
7
RIGHT
DISTRIBUTIVE
LAW
FOR
COMPOSITION
----
13
THE
MATRIX
REPRESENTATION
OF
FORMAL
POWER
SERIES
-
17
ALMOST
UNIT
FORMAL
POWER
SERIES
-
22
ALGEBRAIC
STRUCTURE
OF
X
-
35
ANALYTIC
STRUCTURE
OF
X
-----38
2
2.1
2.2
2.3
2.4
2.5
CALCULUS
OF
FORMAL
POWER
SERIES
-
49
FORMAL
DERIVATIVES
OF
FORMAL
POWER
SERIES
-
49
FORMAL
DIFFERENTIAL
EQUATIONS
AND
THEIR
APPLICATIONS
-
54
ULTRAMETRIC
-
65
SOME
TOPOLOGICAL
STRUCTURE
FOR
X
----
69
THE
UMBRAL
CALCULUS
AND
FORMAL
POWER
SERIES
-
78
3
3.1
3.2
3.3
3.4
APPLICATIONS
OF
FORMAL
POWER
SERIES,
1
-
85
RIORDAN
GROUP
AND
FORMAL
POWER
SERIES
----
85
RIORDAN
INVOLUTIONS
----
92
SOME
SUBGROUPS
OF
THE
RIORDAN
GROUP
----
93
CAYLEY-HAMILTON
THEOREM
AND
FERMAT
'
S
LITTLE
THEOREM
-
96
4
4.1
4.2
4.3
4.4
APPLICATIONS
OF
FORMAL
POWER
SERIES,
II
-
101
FORMAL
POWER
SERIES
AND
SOME
DIFFERENTIAL
EQUATIONS
-
101
FUNCTIONAL
EQUATIONS
AND
FORMAL
POWER
SERIES
-
105
LAGRANGE
INVERSION
-
115
DIFFERENCE
EQUATIONS
AND
FORMAL
POWER
SERIES
-
123
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
GENERAL
COMPOSITION
-
129
INTRODUCTION
----
129
MATRIX
REPRESENTATION
OF
THE
GENERAL
COMPOSITION,
1
-
132
COEFFICIENTS
OF
F
N
(Z)
----
135
THE
GENERAL
COMPOSITION
THEOREM
-
141
THE
GENERAL
CHAIN
RULE
----
150
THE
GENERAL
RIGHT
DISTRIBUTIVE
LAW
-
154
MATRIX
REPRESENTATION
OF
THE
GENERAL
COMPOSITION,
II
-
156
XII
-
CONTENTS
BIBLIOGRAPHY
-
315
6
6.1
6.2
6.3
6.4
FORMAL
ANALYSIS
AND
CLASSICAL
ANALYSIS
-
161
INTRODUCTION
TO
THE
BOUNDARY
BEHAVIOR
----
161
BOUNDARY
BEHAVIOR
AND
FORMAL
ANALYSIS
----
166
BANACH
SPACES
H
P
(P)
AND
P
(P)
----
173
GENERAL
FORMAL
LOGARITHM
-
179
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
FORMAL
LAURENT
SERIES
-
189
SEMIFORMAL
LAURENT
SERIES
----
190
REVERSED
SEMIFORMAL
LAURENT
SERIES
-
199
BASIC
ALGEBRA
OF
FORMAL
LAURENT
SERIES
-
206
COMPOSITION
OF
FORMAL
LAURENT
SERIES
AND
FORMAL
POWER
SERIES
-
217
CANONICAL
MAPPING
AND
DOT
PRODUCT
OF
FORMAL
LAURENT
SERIES
-
224
CANONICAL
MAPPING
AND
MULTIPLICATION
OF
FORMAL
LAURENT
SERIES
-
226
TOPOLOGICAL
SPACES
OF
FORMAL
LAURENT
SERIES
-
233
8
8.1
8.2
8.3
8.4
ITERATION
AND
ITERATIVE
ROOTS
-
245
CONJUGACY
OF
FORMAL
POWER
SERIES
IN
D
----
245
THE
ITERATION
OF
FORMAL
POWER
SERIES
----
264
THE
ITERATIVE
ROOTS
OF
FORMAL
SERIES
IN
D
-
269
SCHRODER
'
S
PROBLEM
-
273
9
9.1
9.2
9.3
9.4
FORMAL
SERIES
AND
GENERAL
EXPONENTS
-
285
INTRODUCTION
----
286
FORMAL
ROOT
SERIES
AND
ITS
ALGORITHM
-
287
POWER
OF
FORMAL
POWER
SERIES
WITH
RATIONAL
EXPONENTS
-
298
THE
REAL
EXPONENTS
OF
FORMAL
POWER
SERIES
-
304
INDEX
-
319 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Gan, Xiao-Xiong |
| author_GND | (DE-588)1164523414 |
| author_facet | Gan, Xiao-Xiong |
| author_role | aut |
| author_sort | Gan, Xiao-Xiong |
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| building | Verbundindex |
| bvnumber | BV047443372 |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)1264223971 (DE-599)DNB1228165742 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV047443372 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:01:33Z |
| indexdate | 2024-07-10T09:12:17Z |
| institution | BVB |
| isbn | 9783110597851 3110597853 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032845516 |
| oclc_num | 1264223971 |
| open_access_boolean | |
| owner | DE-83 DE-11 DE-29T DE-703 |
| owner_facet | DE-83 DE-11 DE-29T DE-703 |
| physical | XII, 323 Seiten 24 cm x 17 cm |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Gan, Xiao-Xiong Verfasser (DE-588)1164523414 aut Formal analysis an introduction Xiao-Xiong Gan Berlin ; Boston De Gruyter [2021] © 2021 XII, 323 Seiten 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics volume 80 Potenzreihe (DE-588)4138577-9 gnd rswk-swf Reihe (DE-588)4049197-3 gnd rswk-swf Laurent-Reihe (DE-588)4192933-0 gnd rswk-swf Potenzreihe (DE-588)4138577-9 s Laurent-Reihe (DE-588)4192933-0 s Reihe (DE-588)4049197-3 s DE-604 Erscheint auch als Online-Ausgabe, PDF 978-3-11-059945-9 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-059860-5 De Gruyter studies in mathematics volume 80 (DE-604)BV000005407 80 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032845516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gan, Xiao-Xiong Formal analysis an introduction De Gruyter studies in mathematics Potenzreihe (DE-588)4138577-9 gnd Reihe (DE-588)4049197-3 gnd Laurent-Reihe (DE-588)4192933-0 gnd |
| subject_GND | (DE-588)4138577-9 (DE-588)4049197-3 (DE-588)4192933-0 |
| title | Formal analysis an introduction |
| title_auth | Formal analysis an introduction |
| title_exact_search | Formal analysis an introduction |
| title_exact_search_txtP | Formal analysis an introduction |
| title_full | Formal analysis an introduction Xiao-Xiong Gan |
| title_fullStr | Formal analysis an introduction Xiao-Xiong Gan |
| title_full_unstemmed | Formal analysis an introduction Xiao-Xiong Gan |
| title_short | Formal analysis |
| title_sort | formal analysis an introduction |
| title_sub | an introduction |
| topic | Potenzreihe (DE-588)4138577-9 gnd Reihe (DE-588)4049197-3 gnd Laurent-Reihe (DE-588)4192933-0 gnd |
| topic_facet | Potenzreihe Reihe Laurent-Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032845516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT ganxiaoxiong formalanalysisanintroduction |