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Oberseminar AG Mathematische Modellierung
Montag, den 14.04.2025 um 17.00 Uhr in B7- Raum 210
Vortrag von Richard Boadi (Clausthal) zum Thema "LP Spaces“.
Abstract: In this talk, we try to explain the principles surrounding L^p spaces and what makes them distinct from other function spaces. We give the motivation for L^p spaces and present the preliminaries, where we look at the definition for $L^1$ spaces, examples and a proof with graphical representation. We further define equivalence class of functions and move on to the definition of L^p and $L^\infinity$ spaces and conclude the preliminaries with the foundations for L^p spaces. Next, we introduce the duality of L^p spaces with it associated theorem. Moreover, we dive into the theorem of reflexivity with a proof, we also look at the definition for convolution with examples and a graphical representation of it and we further add a lemma which establishes it as having a regularising/smoothing effect. We conclude on L^p spaces by introducing smooth approximations where we look at various terminologies associated with it.