Theory Of H Superscript P Spaces

The theory of HP spaces has its origins in discoveries made forty or fifty years ago by such mathematicians as G. H. Hardy, J. E. Littlewood, I. I. Privalov, F. and M. Riesz, V. Smirnov, and G. Szego. Most of this early work is concerned with the properties of individual functions of class HP, and is classical in spirit. In recent years, the development of functional analysis has stimulated new interest in the HP classes as linear spaces. This point of viewhas suggested a variety of natural problems and has provided new methods of attack, leading to important advances in the theory. This book is an account of both aspects of the subject, the classical and the modern. It is intended to provide a convenient source for the older parts of the theory (the work of Hardy and Littlewood, for example), as well as to give a self-contained exposition of more recent developments such as Beurling’s theorem on invariant subspaces, the Macintyre-RogosinskiShapiro-Havinson theory of extremal problems, interpolation theory, the dual space structure of HP with p

The purpose of this text is to present new examples of LP-spaces for 1 ≤ P ≤ ∞. This work has three reasons of interest. First, of course, it provides new LPspaces. Secondly, because certain constructions are based on new ideas and techniques with possibly other applications. Finally, especially in chapters four and five, crucial use is made of certain probabilistic results which have an independent importance.

HP空间理论是函数论、逼近论和调和分析等数学分支的基础之一。本书对这一理论既讨论了早期成果,又阐述了最新发展。

Apart from the underlying theme that all the contributions to this volume pertain to models set in an infinite dimensional space, they differ on many counts. Some were written in the early seventies while others are reports of ongoing research done especially with this volume in mind. Some are surveys of material that can, at least at this point in time, be deemed to have attained a satisfactory solution of the problem, while oth ers represent initial forays into an original and novel formulation. Some furnish alternative proofs of known, and by now, classical results, while others can be seen as groping towards and exploring formulations that have not yet reached a definitive form. The subject matter also has a wide leeway, ranging from solution concepts for economies to those for games and also including representation of preferences and discussion of purely mathematical problems, all within the rubric of choice variables belonging to an infinite dimensional space, interpreted as a commodity space or as a strategy space. Thus, this is a collective enterprise in a fairly wide sense of the term and one with the diversity of which we have interfered as little as possible. Our motivation for bringing all of this work under one set of covers was severalfold.

A comprehensive introduction to the mathematical description of strings, D-branes and the geometry of strongly curved spacetime.

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.

The great success of the experimental research on elementary particles and their qualities during the last years suggests giving a summary of the present situation also in the theoretical description of this important branch of physics. In spite of the precarious situation in this field of theoretical physics I believe I can fully account for this choice and must see that the number of participants and the general interest justify my opinion. In organizing the proceedings it was our prime concern to reduce the delay in editing and also keep down the price. This was possihle only through the assistance of the Springer-Verlag who chose photomechanical method working quicker and cheaper. Therefore we apologize for any mistakes and errors that may occur in the text and formulae. I am very indebted to my secretary, Miss A. SCHMALDIENST and one of my assistants, Dr. H. KÜHNELT, who did an the typing and correcting of the manu scripts with great patience and knowledge.