Integral equations—a reference text - nuovo libro

EAN (ISBN-13): 9789028603936
ISBN (ISBN-10): 902860393X
Copertina rigida
Anno di pubblicazione: 1975
Editore: Springer
464 Pagine
Peso: 0,818 kg
Lingua: eng/Englisch

Libro nella banca dati dal 2007-06-16T13:28:43+02:00 (Rome)
Pagina di dettaglio ultima modifica in 2024-02-24T23:17:29+01:00 (Rome)
ISBN/EAN: 902860393X

ISBN - Stili di scrittura alternativi:
90-286-0393-X, 978-90-286-0393-6
Stili di scrittura alternativi e concetti di ricerca simili:
Autore del libro : mikhlin, koshelev zabreyko
Titolo del libro: intergral, intégral, equations reference integral text, pure and applied mathematics

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Dati dell'editore

Autore: Zabreyko
Titolo: Integral equations—a reference text
Editore: Springer; Springer Netherland
443 Pagine
Anno di pubblicazione: 1975-01-09
Dordrecht; NL
Lingua: Inglese
246,09 € (DE)
252,99 € (AT)
271,50 CHF (CH)
Available
XIX, 443 p.

BB; Hardcover, Softcover / Mathematik; Mathematik; Verstehen; Mathematics; BC

I General Introduction.- §1 Fredholm and Volterra equations.- §2 Other classes of integral equations.- §3 Some inversion formulas.- II The Fredholm Theory.- §1 Basic concepts and the Fredholm theorems.- §2 The solution of Fredholm equations: The method of successive approximation.- §3 The solution of Fredholm equations: Degenerate equations and the general case.- §4 The Fredholm resolvent.- §5 The solution of Fredholm equations: The Fredholm series.- §6 Equations with a weak singularity.- §7 Systems of integral equations.- §8 The structure of the resolvent in the neighbourhood of a characteristic value.- §9 The rate of growth of eigenvalues.- III Symmetric Equations.- §1 Basic properties.- §2 The Hilbert-Schmidt series and its properties.- §3 The classification of symmetric kernels.- §4 Extremal properties of characteristic values and eigenfunctions.- §5 Schmidt kernels and bilinear series for non-symmetric kernels.- §6 The solution of integral equations of the first kind.- IV Integral Equations with Non-Negative Kernels.- §1 Positive eigenvalues.- §2 Positive solutions of the non-homogeneous equation.- §3 Estimates for the spectral radius.- §4 Oscillating kernels.- V Continuous and Compact Linear Operators.- §1 Continuity and compactness for linear integral operators.- §2 Equations of the second kind. The resolvent of an integral operator.- §3 Equations of the second kind with compact operators in a Banach space.- §4 Equations of the second kind with compact operators in a Hilbert space.- §5 Positive operators.- §6 Volterra equations of the second kind.- §7 Equations of the first kind.- VI One-Dimensional Singular Equations.- §1 Basic notions.- §2 Some properties of singular integrals.- §3 Singular operators in functional spaces.- §4Differentiation and integration formulas involving singular integrals.- §5 Regularization.- §6 Closed contours; symbols; Nöther theorems.- §7 The Carleman method for a closed contour.- §8 Systems of singular equations defined on a closed contour.- §9 The open contour case.- §10 Tricomi and Gellerstedt equations.- §11 Equations with degenerate symbol.- §12 Singular equations in generalized function spaces.- VII The Integral Equations of Mathematical Physics.- §1 The integral equations of potential theory.- §2 The application of complex variable to the problems of potential theory in plane regions.- §3 The biharmonic equation and the plane problem in the theory of elasticity.- §4 Potentials for the heat conduction equation.- §5 The generalized Schwarz algorithm.- §6 Application of the theory of symmetric integral equations.- §7 Certain applications of singular integral equations.- VIII Integral Equations with Convolution Kernels.- §1 General introduction.- §2 Examples.- §3 Equations defined on a semi-infinite interval with summable kernels.- §4 Dual equations with summable kernels and their adjoints.- §5 Examples.- §6 Dual equations with kernels of exponential type.- §7 The Wiener-Hopf method.- §8 Equations with degenerate symbol.- §9 Examples.- §10 Systems of equations on a semi-infinite interval.- §11 Equations defined on a finite interval.- IX Multidimensional Singular Equations.- §1 Basic concepts and theorems.- §2 The symbol.- §3 Singular operators in Lp(Em).- §4 Singular integrals over a manifold.- §5 Regularization and Fredholm theorems.- §6 Systems of singular equations.- §7 Singular equations in Lipschitz spaces.- §8 Singular equations on a cylinder.- §9 Singular equations in spaces of generalized functions.- §10 Equationswith degenerate symbol.- §11 Singular integro-differential equations.- §12 Singular equations on a manifold with boundary.- X Non-Linear Integral Equations.- §1 Non-linear integral operators.- §2 The existence and uniqueness of solutions.- §3 The extension and bifurcation of solutions of non-linear integral equations.- References.