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Integral Operators in the Theory of Linear Partial Differential Equations

BuchKartoniert, Paperback
148 Seiten
Englisch
Springererschienen am11.11.2011Softcover reprint of the original 1st ed. 1969
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.mehr
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Produkt

KlappentextThe 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.
Details
ISBN/GTIN978-3-642-64987-5
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2011
Erscheinungsdatum11.11.2011
AuflageSoftcover reprint of the original 1st ed. 1969
ReiheErgebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
Seiten148 Seiten
SpracheEnglisch
Gewicht253 g
IllustrationenX, 148 p.
Artikel-Nr.18231183

Inhalt/Kritik

Inhaltsverzeichnis
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 ofdifferential 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.mehr