Markus Haase, Delft University of Technology, The Netherlands

• Inner product spaces Normed spaces Distance and approximation Continuity and compactness Banach spaces The contraction principle The Lebesgue spaces Hilbert space fundamentals Approximation theory and Fourier analysis Sobolev spaces and the Poisson problem Operator theory I Operator theory II Spectral theory of compact self-adjoint operators Applications of the spectral theorem Baire's theorem and its consequences Duality and the Hahn-Banach theorem Historical remarks Background The completion of a metric space Bernstein's proof of Weierstrass' theorem Smooth cutoff functions Some topics from Fourier analysis General orthonormal systems Bibliography Symbol index Subject index Author index

Markus Haase’s beautiful book lives up to its promise: it provides a well-structured and gentle introduction to the fundamental concepts of functional analysis…The presentation is clear, the applications are insightful, and the large collection of exercises allow us to deepen the study of the presented material. Graduate students, as well as interested undergraduate students can easily profit from this well-written book." - Béla Gábor Pusztai, ACTA Sci. Math

Markus Haase, Delft University of Technology, The Netherlands

• Inner product spaces Normed spaces Distance and approximation Continuity and compactness Banach spaces The contraction principle The Lebesgue spaces Hilbert space fundamentals Approximation theory and Fourier analysis Sobolev spaces and the Poisson problem Operator theory I Operator theory II Spectral theory of compact self-adjoint operators Applications of the spectral theorem Baire's theorem and its consequences Duality and the Hahn-Banach theorem Historical remarks Background The completion of a metric space Bernstein's proof of Weierstrass' theorem Smooth cutoff functions Some topics from Fourier analysis General orthonormal systems Bibliography Symbol index Subject index Author index

Markus Haase’s beautiful book lives up to its promise: it provides a well-structured and gentle introduction to the fundamental concepts of functional analysis…The presentation is clear, the applications are insightful, and the large collection of exercises allow us to deepen the study of the presented material. Graduate students, as well as interested undergraduate students can easily profit from this well-written book." - Béla Gábor Pusztai, ACTA Sci. Math

Markus Haase, Delft University of Technology, The Netherlands

• Inner product spaces Normed spaces Distance and approximation Continuity and compactness Banach spaces The contraction principle The Lebesgue spaces Hilbert space fundamentals Approximation theory and Fourier analysis Sobolev spaces and the Poisson problem Operator theory I Operator theory II Spectral theory of compact self-adjoint operators Applications of the spectral theorem Baire's theorem and its consequences Duality and the Hahn-Banach theorem Historical remarks Background The completion of a metric space Bernstein's proof of Weierstrass' theorem Smooth cutoff functions Some topics from Fourier analysis General orthonormal systems Bibliography Symbol index Subject index Author index

Markus Haase’s beautiful book lives up to its promise: it provides a well-structured and gentle introduction to the fundamental concepts of functional analysis…The presentation is clear, the applications are insightful, and the large collection of exercises allow us to deepen the study of the presented material. Graduate students, as well as interested undergraduate students can easily profit from this well-written book." - Béla Gábor Pusztai, ACTA Sci. Math