Abstract
The goal of this chapter is to recall, without proof, the main results in functional analysis: classical theorems about Fréchet, Hilbert, and Banach spaces, as well as fixed point theorems and an introduction to spectral theory. This is complemented by the main definitions in distributions theory, including results about the Fourier transform.
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References
Alazard, T.: Analyse et équations aux dérivées partielles. Lectures Notes. Available at http://talazard.perso.math.cnrs.fr (2020)
Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011)
Hörmander, L.: The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis. Classics in Mathematics. Springer, Berlin (2003) (Reprint of the second (1990) edition [Springer, Berlin; MR1065993 (91m:35001a)].)
Rudin, W.: Functional Analysis. International Series in Pure and Applied Mathematics, 2nd edn. McGraw-Hill, Inc., New York (1991)
Zuily, C.: Problems in Distributions and Partial Differential Equations. North-Holland Mathematics Studies, vol. 143. North-Holland Publishing Co./Hermann, Amsterdam/Paris (1988) (Translated from the French.)
Zuily, C.: Distributions et équations aux dérivées partielles. Dunod, Paris (2002)
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Alazard, T., Zuily, C. (2020). Elements of Functional Analysis and Distributions. In: Tools and Problems in Partial Differential Equations. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-50284-3_1
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DOI: https://doi.org/10.1007/978-3-030-50284-3_1
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