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Based on a third-year course for French students of physics, this book is a graduate text in functional analysis emphasizing applications to physics. It introduces Lebesgue integration, Fourier and Laplace transforms, Hilbert space theory, theory of distribution a la Laurent Schwartz, linear operators, and spectral theory. It contains numerous examples and completely worked out exercises.
Measure and Integration. Lebesgue Spaces. Hilbert Spaces. Distributions. Linear Operators. References. Index.