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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. --- Espais de Banach --- Anàlisi funcional

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The book is devoted to the study of constrained minimization problems on closed and convex sets in Banach spaces with a Frechet differentiable objective function. Such problems are well studied in a finite-dimensional space and in an infinite-dimensional Hilbert space. When the space is Hilbert there are many algorithms for solving optimization problems including the gradient projection algorithm which is one of the most important tools in the optimization theory, nonlinear analysis and their applications. An optimization problem is described by an objective function and a set of feasible points. For the gradient projection algorithm each iteration consists of two steps. The first step is a calculation of a gradient of the objective function while in the second one we calculate a projection on the feasible set. In each of these two steps there is a computational error. In our recent research we show that the gradient projection algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. It should be mentioned that the properties of a Hilbert space play an important role. When we consider an optimization problem in a general Banach space the situation becomes more difficult and less understood. On the other hand such problems arise in the approximation theory. The book is of interest for mathematicians working in optimization. It also can be useful in preparation courses for graduate students. The main feature of the book which appeals specifically to this audience is the study of algorithms for convex and nonconvex minimization problems in a general Banach space. The book is of interest for experts in applications of optimization to the approximation theory. In this book the goal is to obtain a good approximate solution of the constrained optimization problem in a general Banach space under the presence of computational errors. It is shown that the algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems are studied in Chapter 3. In Chapter 4 we study continuous algorithms for minimization problems under the presence of computational errors. The algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems are studied in Chapter 3. In Chapter 4 we study continuous algorithms for minimization problems under the presence of computational errors.

Numerical methods of optimisation --- Operational research. Game theory --- Numerical analysis --- Computer. Automation --- automatisering --- wiskunde --- numerieke analyse --- Banach spaces. --- Mathematical optimization. --- Optimització matemàtica --- Espais de Banach

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This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Functional analysis. --- Fourier analysis. --- Harmonic analysis. --- Operator theory. --- Mathematical analysis. --- Functional Analysis. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Operator Theory. --- Analysis. --- Anàlisi harmònica --- Teoria d'operadors --- Anàlisi de Fourier --- Anàlisi matemàtica --- Anàlisi funcional --- Espais de Banach

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Teoria d'operadors --- Espais de Hilbert --- Anàlisi funcional --- Àlgebres d'operadors --- Equacions d'evolució no lineal --- Operadors diferencials --- Operadors integrals --- Operadors lineals --- Operadors no lineals --- Operadors pseudodiferencials --- Semigrups d'operadors --- Teoria dels operadors --- Espais de Banach --- Hiperespai --- Teoria espectral (Matemàtica) --- Espai de Hilbert --- Hilbert space. --- Operator theory. --- Functional analysis --- Banach spaces --- Hyperspace --- Inner product spaces

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Hilbert space. --- Banach spaces --- Hyperspace --- Inner product spaces --- Problemes inversos (Equacions diferencials) --- Espais de Hilbert --- Operadors lineals --- Teoria d'operadors --- Operadors de Calderón-Zygmund --- Operadors autoadjunts --- Operadors de Toeplitz --- Espai de Hilbert --- Espais de Banach --- Hiperespai --- Teoria espectral (Matemàtica) --- Equacions diferencials