Integral operators in the theory of linear partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1971
|
| Edition: | 3. print. |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
23 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 143 S. |
| ISBN: | 354004468X 038704468X |
Staff View
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| 245 | 1 | 0 | |a Integral operators in the theory of linear partial differential equations |
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1971 | |
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Record in the Search Index
| _version_ | 1804136090951483392 |
|---|---|
| adam_text | Contents
Introduction 1
I. Differential equations in two variables with entire coefficients 9
§ 1. A representation of solutions of partial differential equations . ... 10
§ 2. The integral operator of the first kind 12
§3. Further representations of integral operators 15
§ 4. A representation of the operator of the first kind in terms of integrals 17
§ 5. Properties of the integral operator of the first kind 19
§ 6. Some further properties of the integral operator of the first kind . . 20
§7. The differential equation J,F + F(r*) V — 0 27
§ 8. Integral operators of exponential type 31
§9. The differential equation A% p + N(x)y — 0 33
§ 10. Differential equations of higher order 35
II. Harmonic functions in three variables 38
§ 1. Preliminaries 38
§ 2. Characteristic space (i3 39
§ 3. Harmonic functions with rational B3 associates 43
§ 4. Period functions 50
§ 5. Relations between coefficients of a series development of a harmonic
function and its singularities 54
§ 6. Another type of integral representations of harmonic functions ... 57
§ 7. The behavior in the large of functions of the class S(E, f0, £,) with a
rational associate / (J) 60
III. Differential equations in three variables 63
§ 1. An integral operator generating solutions of the equation
A3y + A(r*) X ¦ Vy + C(r2) yi = 0 64
§ 2. A series expansion for solutions of the equation
^3y + A{r*) X Vy + C(r ) xf = 0 66
§ 3. An integral operator generating solutions of the equation
Aty + F(y,z)y =0 68
§ 4. A second integral operator generating solutions of the equation
J,y+ F(y, *)y = 0 71
§ 5. An integral operator generating solutions of the equation
V* + Wv + Vzz + F(y *) V = 0 74
§ 6. An integral operator generating solutions of the equation
g VhV, p+hi Vl4 + li p = 0 78
X Contents
IV. Systems of differential equations 81
§ 1. Harmonic vectors of three variables. Preliminaries 81
§ 2. Harmonic vectors in the large and their representation as integrals . 83
§ 3. Integrals of harmonic vectors 86
§ 4. Relations between integrals of algebraic harmonic vectors in three
variables and integrals of algebraic functions of a complex variable 89
§ 5. Generalization of the residue theorems to the case of the equation
A,y + F(r*) y = 0 92
§ 6. An operator generating solutions of a system of partial differential
equations 96
V. Equations of mixed type and elliptic equations with singular and non
analytic coefficients 106
§ 1. Introduction. The simplified case of equations of mixed type .... 106
§ 2. A generalization of the representation (1.12) of solutions of the
equation (1.6) 108
§3. The operator (1.11b) in the general case 112
§ 4. Generating functions analogous to solutions of the hypergeometric
equation 117
§5. On the solution of the initial value problem in the large 120
§ 6. Generalized Cauchy Riemann equations 122
§ 7. The differential equation Atxp N(x)y = 0 with a new type of singu¬
larity of N 125
§ 8. An integral operator for equations with non analytic coefficients . . 127
Bibliography 132
Subject Index 145
|
| adam_txt |
Contents
Introduction 1
I. Differential equations in two variables with entire coefficients 9
§ 1. A representation of solutions of partial differential equations . . 10
§ 2. The integral operator of the first kind 12
§3. Further representations of integral operators 15
§ 4. A representation of the operator of the first kind in terms of integrals 17
§ 5. Properties of the integral operator of the first kind 19
§ 6. Some further properties of the integral operator of the first kind . . 20
§7. The differential equation J,F + F(r*) V — 0 27
§ 8. Integral operators of exponential type 31
§9. The differential equation A%\p + N(x)y — 0 33
§ 10. Differential equations of higher order 35
II. Harmonic functions in three variables 38
§ 1. Preliminaries 38
§ 2. Characteristic space (i3 39
§ 3. Harmonic functions with rational B3 associates 43
§ 4. Period functions 50
§ 5. Relations between coefficients of a series development of a harmonic
function and its singularities 54
§ 6. Another type of integral representations of harmonic functions . 57
§ 7. The behavior in the large of functions of the class S(E, f0, £,) with a
rational associate / (J) 60
III. Differential equations in three variables 63
§ 1. An integral operator generating solutions of the equation
A3y + A(r*) X ¦ Vy + C(r2) yi = 0 64
§ 2. A series expansion for solutions of the equation
^3y + A{r*) X Vy + C(r') xf = 0 66
§ 3. An integral operator generating solutions of the equation
Aty + F(y,z)y =0 68
§ 4. A second integral operator generating solutions of the equation
J,y+ F(y, *)y = 0 71
§ 5. An integral operator generating solutions of the equation
V* + Wv + Vzz + F(y *) V = 0 74
§ 6. An integral operator generating solutions of the equation
g"'VhV, p+hi'Vl4 + li p = 0 78
X Contents
IV. Systems of differential equations 81
§ 1. Harmonic vectors of three variables. Preliminaries 81
§ 2. Harmonic vectors in the large and their representation as integrals . 83
§ 3. Integrals of harmonic vectors 86
§ 4. Relations between integrals of algebraic harmonic vectors in three
variables and integrals of algebraic functions of a complex variable 89
§ 5. Generalization of the residue theorems to the case of the equation
A,y + F(r*) y = 0 92
§ 6. An operator generating solutions of a system of partial differential
equations 96
V. Equations of mixed type and elliptic equations with singular and non
analytic coefficients 106
§ 1. Introduction. The simplified case of equations of mixed type . 106
§ 2. A generalization of the representation (1.12) of solutions of the
equation (1.6) 108
§3. The operator (1.11b) in the general case 112
§ 4. Generating functions analogous to solutions of the hypergeometric
equation 117
§5. On the solution of the initial value problem in the large 120
§ 6. Generalized Cauchy Riemann equations 122
§ 7. The differential equation Atxp \ N(x)y = 0 with a new type of singu¬
larity of N 125
§ 8. An integral operator for equations with non analytic coefficients . . 127
Bibliography 132
Subject Index 145 |
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| any_adam_object_boolean | 1 |
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| author_GND | (DE-588)118656074 |
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| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)439747559 (DE-599)BVBBV022117167 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. print. |
| format | Book |
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| id | DE-604.BV022117167 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:01Z |
| indexdate | 2024-07-09T20:50:53Z |
| institution | BVB |
| isbn | 354004468X 038704468X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015332031 |
| oclc_num | 439747559 |
| open_access_boolean | |
| owner | DE-706 DE-188 |
| owner_facet | DE-706 DE-188 |
| physical | 143 S. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Bergman, Stefan 1898-1977 Verfasser (DE-588)118656074 aut Integral operators in the theory of linear partial differential equations 3. print. Berlin [u.a.] Springer 1971 143 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 23 Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Integraloperator (DE-588)4131247-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Integraloperator (DE-588)4131247-8 s 1\p DE-604 Lineare partielle Differentialgleichung (DE-588)4167708-0 s 2\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete 23 (DE-604)BV005871160 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bergman, Stefan 1898-1977 Integral operators in the theory of linear partial differential equations Ergebnisse der Mathematik und ihrer Grenzgebiete Partielle Differentialgleichung (DE-588)4044779-0 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Integraloperator (DE-588)4131247-8 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4167708-0 (DE-588)4131247-8 |
| title | Integral operators in the theory of linear partial differential equations |
| title_auth | Integral operators in the theory of linear partial differential equations |
| title_exact_search | Integral operators in the theory of linear partial differential equations |
| title_exact_search_txtP | Integral operators in the theory of linear partial differential equations |
| title_full | Integral operators in the theory of linear partial differential equations |
| title_fullStr | Integral operators in the theory of linear partial differential equations |
| title_full_unstemmed | Integral operators in the theory of linear partial differential equations |
| title_short | Integral operators in the theory of linear partial differential equations |
| title_sort | integral operators in the theory of linear partial differential equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Integraloperator (DE-588)4131247-8 gnd |
| topic_facet | Partielle Differentialgleichung Lineare partielle Differentialgleichung Integraloperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT bergmanstefan integraloperatorsinthetheoryoflinearpartialdifferentialequations |