Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
Integral Operators in the Theory of Linear Partial Differential Equations
.
Bookmark this Record
Catalogue Record 41918
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 41918
.
Reviews
Catalogue Record 41918
.
British Library
Resolver for RSN-41918
Google Scholar
Resolver for RSN-41918
WorldCat
Resolver for RSN-41918
Catalogo Nazionale SBN
Resolver for RSN-41918
GoogleBooks
Resolver for RSN-41918
ICTP Library
Resolver for RSN-41918
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
515
Title
Integral Operators in the Theory of Linear Partial Differential Equations ([EBook]) / by Stefan Bergman.
Author
Bergman, Stefan. , 1898-1977
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : Springer , 1961.
Physical Details
X, 148 pages : online resource.
Series
Ergebnisse der Mathematik und ihrer Grenzgebiete
0071-1136 ; ; 23
ISBN
9783642649851
Summary Note
The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information.:
Contents note
I. Differential equations in two variables with entire coefficients -- § 1. A representation of solutions of partial differential equations -- § 2. The integral operator of the first kind -- § 3. Further representations of integral operators -- § 4. A representation of the operator of the first kind in terms of integrals -- § 5. Properties of the integral operator of the first kind -- § 6. Some further properties of the integral operator of the first kind -- § 7. The differential equation ?2V + F(r2) V = 0 -- § 8. Integral operators of exponential type -- § 9. The differential equation ?2? + N (x) ? = 0 -- § 10. Differential equations of higher order -- II. Harmonic functions in three variables -- § 1. Preliminaries -- § 2. Characteristic space ?3 -- § 3. Harmonic functions with rational B3-associates -- § 4. Period functions -- § 5. Relations between coefficients of a series development of a harmonic function and its singularities -- § 6. Another type of integral representations of harmonic functions -- § 7. The behavior in the large of functions of the class S (E, ?0, ?1) with a rational associate f (?) -- III. Differential equations in three variables -- § 1. An integral operator generating solutions of the equation ?3? + A (r2) X · ? ? + C (r2) ? = 0 -- § 2. A series expansion for solutions of the equation ?3? + A (r2) X · ? ? + C (r2) ? = 0 -- § 3. An integral operator generating solutions of the equation ?3? + F (y, z) ? = 0 -- § 4. A second integral operator generating solutions of the equation ?3? + F (y, z) ? = 0 -- § 5. An integral operator generating solutions of the equation ?x + ?yy + ?zz + F (y, z) ? = 0 -- § 6. An integral operator generating solutions of the equation g???????+h????+k? = 0 -- IV. Systems of differential equations -- § 1. Harmonic vectors of three variables. Preliminaries -- § 2. Harmonic vectors in the large and their representation as integrals -- § 3. Integrals of harmonic vectors -- § 4. Relations between integrals of algebraic harmonic vectors in three variables and integrals of algebraic functions of a complex variable -- § 5. Generalization of the residue theorems to the case of the equation ?3? + F (r2) ? = 0 -- § 6. An operator generating solutions of a system of partial differential equations -- V. Equations of mixed type and elliptic equations with singular and non-analytic -- § 1. Introduction. The simplified case of equations of mixed type -- § 2. A generalization of the representation (1.12) of solutions of the equation (1.6) -- § 3. The operator (1.11b) in the general case -- § 4. Generating functions analogous to solutions of the hypergeometric equation -- § 5. On the solution of the initial value problem in the large -- § 6. Generalized Cauchy-Riemann equations -- § 7. The differential equation ?2? + N(x)? = 0 with a new type of singularity of N -- § 8. An integral operator for equations with non-analytic coefficients.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-642-64985-1
Links to Related Works
Subject References:
Analysis
.
Analysis (Mathematics)
.
Mathematical analysis
.
Mathematics
.
Partial differential equations
.
Authors:
Bergman, Stefan. 1898-1977
.
Bergman, Stefan, 1898-1977.
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Ergebnisse der Mathematik und ihrer Grenzgebiete
.
Classification:
515
.
.
ISBD Display
Catalogue Record 41918
.
Tag Display
Catalogue Record 41918
.
Related Works
Catalogue Record 41918
.
Marc XML
Catalogue Record 41918
.
Add Title to Basket
Catalogue Record 41918
.
Catalogue Information 41918
Beginning of record
.
Catalogue Information 41918
Top of page
.
Download Title
Catalogue Record 41918
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
41918
1
41918
-
2
41918
-
3
41918
-
4
41918
-
5
41918
-
Quick Search
Search for