Algebraic Analysis: Mathematics and its Applications, cartea 25
Autor D. Przeworska-Rolewiczen Limba Engleză Paperback – 26 sep 2011
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Specificații
ISBN-13: 9789401071390
ISBN-10: 940107139X
Pagini: 648
Ilustrații: 620 p.
Dimensiuni: 152 x 229 x 34 mm
Greutate: 0.85 kg
Ediția:Softcover reprint of the original 1st ed. 1988
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and its Applications
Locul publicării:Dordrecht, Netherlands
ISBN-10: 940107139X
Pagini: 648
Ilustrații: 620 p.
Dimensiuni: 152 x 229 x 34 mm
Greutate: 0.85 kg
Ediția:Softcover reprint of the original 1st ed. 1988
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and its Applications
Locul publicării:Dordrecht, Netherlands
Public țintă
ResearchCuprins
1. Fundamental properties of linear operators in lineal spaces.- 1.1. Groups and rings.- 1.2. Linear spaces.- 1.3. Linear operators and linear functionals.- 1.4. Eigenspaces and principal spaces. Algebraic operators. Volterra operators.- 1.5. Conjugate spaces and conjugate operators.- 2. Calculus of right invertible operators.- 2.1. Properties of right inverses. Indefinite integrals.- 2.2. Initial operators. Taylor—Gontcharov formula. Definite integrals.- 2.3. Exponentials, sine and cosine operators and Volterra right inverses.- 2.4. D-polynomials.- 2.5. Remarks on left invertible operators.- 3. General solution of equations with right invertible operators.- 3.1. Equations of order one with non-commutative coefficients.- 3.2. Equations of higher order with non-commutative coefficients.- 3.3. Equations with stationary coefficients.- 3.4. Equations with scalar coefficients. Operational calculus of right invertible operators. D-hull.- 3.5. Systems of equations with scalar coefficients.- 3.6. General solution of equations with left invertible operators.- 4. Initial and boundary value problems.- 4.1. Well-posed and ill-posed initial value problems.- 4.2. Hyperbolic equations.- 4.3. Elliptic and polyharmonic equations.- 4.4. Differential equations with delayed and advanced argument.- 4.5. Equations with involutions of order n.- 4.6. Well-posed and ill-posed boundary value problems.- 5. Periodic operators and elements. Shift operators. Shift invariant spaces.- 5.1. Periodic operators and elements.- 5.2. R-shifts and D-shifts.- 5.3. Existence of periodic solutions.- 5.4. Canonical mapping.- 5.5. Boundary value problems for stationary linear systems with shifts.- 6. D-algebras.- 6.1. Classification and examples of D-algebras.- 6.2. Integration. Exponentials. Trigonometricidentity.- 6.3. Constants variation method. Wro?ski theorems.- 6.4. Fourier method.- 6.5. Green formulae. Picone identity. Euler—Lagrange equation.- 7. Perturbations and nonlinear problems.- 7.1. Finite dimensional perturbations.- 7.2. Perturbations by means of right inverses.- 7.3. Quasi-linear and nonlinear problems.- 7.4. Method of variables separable.- 8. Why using metric properties in algebraic analysis?.- 8.1. Right invertible operators in linear metric spaces.- 8.2. Canonical mapping and semigroups.- 8.3, Perturbations and periodic problems.- 8.4. Bielecki method and its applications.- 9. Miscellanea.- 9.1. Accelerating convergence of orthonormal series.- 9.2. Von Trotha principle of contractive mappings.- 9.3. Linear systems. F1-controllability.- 9.4. Dualities and conjugate systems.- Authors index.- List of symbols.