Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods
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- Artikel-Nr.: 10440561
Beschreibung
Introduction.- Spaces of Test Functions.- Schwartz Distributions.- Calculus for Distributions.- Distributions as Derivatives of Functions.- Tensor Products.- Convolution Products.- Applications of Convolution.- Holomorphic Functions.- Fourier Transformations.- Distributions as Boundary Values of Analytic Functions.- Other Spaces of Generalized Functions.- Sobolev Spaces.- Hilbert Spaces: A Brief Historical Introduction.- Inner Product Spaces and Hilbert Spaces.- Geometry of Hilbert Spaces.- Separable Hilbert Spaces.- Direct Sums and Tensor Products.- Topological Aspects.- Linear Operators.- Quadratic Forms.- Bounded Linear Operators.- Special Classes of Linear Operators.- Elements of Spectral Theory.- Compact Operators.- Hilbert-Schmidt and Trace Class Operators.- The Spectral Theorem.- Some Applications of the Spectral Representation.- Spectral Analysis in Rigged Hilbert Spaces.- Operator Algebras and Positive Mappings.- Positive Mappings in Quantum Physics.- Introduction.- Direct Methods in the Calculus of Variations.- Differential Calculus on Banach Spaces and Extrema of Functions.- Constrained Minimization Problems (Method of Lagrange Multipliers).- Boundary and Eigenvalue Problems.- Density Functional Theory of Atoms and Molecules.- Appendices.- Index.
Eigenschaften
Breite: | 170 |
Gewicht: | 1092 g |
Höhe: | 248 |
Länge: | 36 |
Seiten: | 598 |
Sprachen: | Englisch |
Autor: | Erwin Brüning, Philippe Blanchard |
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