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Mathematical inequalities : a perspective
\"Provides an overview of the expanding field of mathematical inequalities and their applications. Instead of focusing on narrow treatments of various mathematical inequalities, the authors present a number of classical and recent results across the field, covering integral inequalities, discrete inequalities, and inequalities in abstract spaces. They also make new connections and investigate intimate relationships between inequalities ... The text offers simple proofs for young researchers yet incorporates sufficient detail to appeal to experts and graduate students in real and functional analysis\"-- Provided by publisher.
Book
Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations
In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin).
We establish the following results:
The key tools behind our results
are limiting interpolation techniques and new characterizations of Besov and Sobolev norms in terms of the behavior of the Fourier
transforms for functions such that their Fourier transforms are of monotone type or lacunary series.
eBook
Embeddings of Decomposition Spaces
Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two such spaces, is there an
embedding between the two?
A decomposition space
We establish readily verifiable criteria which ensure the
existence of a continuous inclusion (“an embedding”)
In a nutshell, in order to apply the embedding results presented in this
article, no knowledge of Fourier analysis is required; instead, one only has to study the geometric properties of the involved
coverings, so that one can decide the finiteness of certain sequence space norms defined in terms of the coverings.
These
sufficient criteria are quite sharp: For almost arbitrary coverings and certain ranges of
We also prove a
The resulting embedding theory is illustrated by applications
to
eBook
Applied nonlinear functional analysis : an introduction
The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis.
Contents
Basic Topology
Measure Theory
Basic Functional Analysis
Banach Spaces of Functions and Measures
Convex Functions – Nonsmooth Analysis
Nonlinear Analysis
eBook
Scientific literacy for participation : a systemic functional approach to analysis of school science discourses
Scientific literacy is approached on the premise that language is key to understand the nature of both learning and participation, in scientists{u2019} practices as well as in liberal education for citizenship. Some of the questions that are addressed in the book are: {u2022} What does it take to be able to participate in different arenas in society involving science? {u2022} How does everyday language relate to scientific language? {u2022} How can students{u2019} texts be analyzed to gain insights into their learning? {u2022} How can images be analyzed alongside verbal language? This book offers a thorough introduction to key ideas in M. A. K. Halliday{u2019}s systemic functional grammar through examples and practical analysis. Detailed analysis is offered of science textbooks and curriculum documents, classroom talk, experimental work, and students{u2019} discussions of complex environmental issues. Further, an analytical model guiding the design and analysis of science learning discourses is introduced. The book starts with introducing excerpts from whole-class discussions, group work, experimental reports and textbooks as text-in-context. From this starting point, key aspects of language are carefully explained. The role of grammatical metaphor in the development of science knowledge is an important topic throughout the book. Tools for analyzing multimodal representations, intertextuality and multiple voices are also among the topics covered for understanding and analyzing school science discourses.
Book
Singular integrals in quantum Euclidean spaces
We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of
noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes’ pseudodifferential calculus for
rotation algebras, thanks to a new form of Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution
kernels. We deduce
eBook
Advances in ultrametric analysis : 14th International Conference, p-adic Functional Analysis, June 30-July 4, 2016, Université d'Auvergne, Aurillac, France
This book contains the proceedings of the 14th International Conference on $p$-adic Functional Analysis, held from June 30-July 5, 2016, at the Universite d'Auvergne, Aurillac, France. Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of p -adic series, rational maps on the projective line over Q p , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, G -modules with a convex base, non-compact Trace class operators and Schatten-class operators in p -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, p -adic Nevanlinna theory and applications, and sub-coordinate representation of p -adic functions. Moreover, a paper on the history of p -adic analysis with a comparative summary of non-Archimedean fields is presented.Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
eBook
Quadratic Vector Equations On Complex Upper Half-Plane
The authors consider the nonlinear equation -\\frac 1m=z+Sm with a parameter z in the complex upper half plane \\mathbb H , where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in \\mathbb H is unique and its z-dependence is conveniently described as the Stieltjes transforms of a family of measures v on \\mathbb R. In a previous paper the authors qualitatively identified the possible singular behaviors of v: under suitable conditions on S we showed that in the density of v only algebraic singularities of degree two or three may occur. In this paper the authors give a comprehensive analysis of these singularities with uniform quantitative controls. They also find a universal shape describing the transition regime between the square root and cubic root singularities. Finally, motivated by random matrix applications in the authors' companion paper they present a complete stability analysis of the equation for any z\\in \\mathbb H, including the vicinity of the singularities.
eBook