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We begin by recalling some basic notions of functional analysis. A measurable function belongs to the Lebesgue space if
A Hilbert space is a space where an inner product is defined. In particular, the space is a Hilbert space, where the inner product of 2 functions and is defined as:
In this presentation we work with functions defined on but that take values in Hence denotes the complex conjugate of We say that 2 functions are orthogonal if their inner product is zero. A function is Hölder continuous of order at point if :
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