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This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. ContentsIntroductionLinear operatorsBasic notations and resultsBasesSemi-groupsDiscrete operator and denseness of the generalized eigenvectorsFrames in Hilbert spacesSummability of seriesν-convergence operatorsΓ-hypercyclic set of linear operatorsAnalytic operators in Béla Szökefalvi-Nagy's senseBases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

Banach spaces. --- Functions of complex variables --- Generalized spaces --- Topology

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The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.

Metric spaces. --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Mathematics. --- Mathematics, general. --- Math --- Science

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The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich - one of the leading category theorists of the world - to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader

Categories (Mathematics) --- Topological spaces --- Metric spaces --- Topology --- Spaces, Metric --- Generalized spaces --- Set theory --- Spaces, Topological

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This book presents a theory motivated by the spaces LP, 0 ≤ p < l. These spaces are not locally convex, so the methods usually encountered in linear analysis (particularly the Hahn-Banach theorem) do not apply here. Questions about the size of the dual space are especially important in the non-locally convex setting, and are a central theme. Several of the classical problems in the area have been settled in the last decade, and a number of their solutions are presented here. The book begins with concrete examples (lp, LP, L0, HP) before going on to general results and important counterexamples. An F-space sampler will be of interest to research mathematicians and graduate students in functional analysis.

Function spaces. --- Metric spaces. --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Spaces, Function --- Functional analysis

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Linear algebra is a fundamental area of mathematics, and arguably the most powerful mathematic tool ever deployed. This book uses numerous examples, question and answer sections, and historical biographies to provide an introduction to linear algebra for undergraduates in mathematics, the physical sciences and engineering.

Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology