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Functional analysis. --- Functional analysis

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This monograph provides a comprehensive study of a typical and novel function space, known as the $mathcal{N}_p$ spaces. These spaces are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball, and the authors also explore composition operators and weighted composition operators on these spaces. The book covers a significant portion of the recent research on these spaces, making it an invaluable resource for those delving into this rapidly developing area. The authors introduce various weighted spaces, including the classical Hardy space $H^2$, Bergman space $B^2$, and Dirichlet space $mathcal{D}$. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces $mathcal{B}^p$ and Bergman-type spaces $A^p$. Additionally, the authors extend their analysis beyond the open unit disk $mathbb{D}$ and open unit ball $mathbb{B}$ by presenting families of entire functions in the complex plane $mathbb{C}$ and in higher dimensions. The Theory of $mathcal{N}_p$ Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.

Functional analysis. --- Functional Analysis.

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Functional analysis. --- Functional analysis.

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"Die lineare Funktionalanalysis ist ein weitgehend kanonisiertes Teilgebiet der Mathematik, das in seiner Synthese von Algebra, Topologie und Analysis von großem ästhetischem Reiz ist. Das vorliegende Buch gibt eine geschlossene, geschickt aufgebaute und gut geschriebene Einführung in dieses Gebiet, die auch die erforderlichen Kenntnisse aus der Maßtheorie ... [in eigenen Anhängen] bereitstellt." (Internationale Mathematische Nachrichten) Das Buch ist besonders geeignet für Leser, die schnell zu den zentralen Aussagen vorstoßen wollen. Es enthält die vollständigen Beweise aller mathematischen Sätze und darüberhinaus zahlreiche Aufgaben, die meisten mit Lösungen. Für die nun vorliegende sechste Auflage wurde das Buch nochmals überarbeitet und wird damit zu einem Standardwerk auf dem Gebiet der Funktionalanalysis, wobei es sich insbesondere an Leser richtet, die an Anwendungen auf Differentialgleichungen interessiert sind.

Functional analysis. --- Functional Analysis.

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The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved.A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state n

Functional equations. --- Equations, Functional --- Functional analysis