Continuous Transformations in Analysis by Tibor Rado
The general objective of this treatise is to give a systematic presenta tion of some of the topological and measure-theoretical foundations of the theory of real-valued functions of several real variables, with particular emphasis upon a line of thought initiated by BANACH, GEOCZE, LEBESGUE, TONELLI, and VITALI. To indicate a basic feature in this line of thought, let us consider a real-valued continuous function I(u) of the single real variable tt. Such a function may be thought of as defining a continuous translormation T under which x = 1 (u) is the image of u. About thirty years ago, BANACH and VITALI observed that the fundamental concepts of bounded variation, absolute continuity, and derivative admit of fruitful geometrical descriptions in terms of the transformation T: x = 1 (u) associated with the function 1 (u). They further noticed that these geometrical descriptions remain meaningful for a continuous transformation T in Euclidean n-space Rff, where T is given by a system of equations of the form 1-/(1 ff) X-I U, . . . ,tt ,. ", and n is an arbitrary positive integer. Accordingly, these geometrical descriptions can be used to define, for continuous transformations in Euclidean n-space Rff, n-dimensional concepts 01 bounded variation and absolute continuity, and to introduce a generalized Jacobian without reference to partial derivatives. These ideas were further developed, generalized, and modified by many mathematicians, and significant applications were made in Calculus of Variations and related fields along the lines initiated by GEOCZE, LEBESGUE, and TONELLI.-
Complex Abelian Varieties
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Entire Functions of Several Complex Variables
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Finite Groups I
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Markov Processes
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Random Perturbations of Dynamical Systems
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Global Analysis of Minimal Surfaces
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Vorlesungen über Differenzenrechnung
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Minimal Surfaces
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Vorlesungen uber Topologie
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Harmonic Analysis on Semi-Simple Lie Groups II
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Einleitung in die Mengenlehre
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Lagerungen in der Ebene auf der Kugel und im Raum
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Algebraic Systems
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Aufgaben und Lehrsätze aus der Analysis
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Die Grundlagen der Quantenmechanik
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Anfangswertprobleme bei Partiellen Differentialgleichungen
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Foundations of the Mathematical Theory of Electromagnetic Waves
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Equations Differentielles Operationnelles
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Topology and Geometry of Intersections of Ellipsoids in R^n
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Die Gruppentheoretische Methode in der Quantenmechanik
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Theta Functions
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Markov Processes, Structure and Asymptotic Behavior
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Non-Homogeneous Boundary Value Problems and Applications
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Endliche Gruppen I
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Reelle Funktionen
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Regularity of Minimal Surfaces
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Topological Vector Spaces II
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An Introduction to the Theory of Multipliers
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Baer *-Rings
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Classification Theory of Riemann Surfaces
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Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces
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Harmonic Analysis on Semi-Simple Lie Groups I
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Moderne Algebra
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Die Grundlagen der Theorie der Markoffschen Prozesse
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Nevanlinna Theory in Several Complex Variables and Diophantine Approximation
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Der Absolute Differentialkalkül und seine Anwendungen in Geometrie und Physik
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Abstract Harmonic Analysis
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Quasikonforme Abbildungen
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Vorlesungen über Himmelsmechanik
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Methoden der Mathematischen Physik
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Analytische Dynamik der Punkte und Starren Körper
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Grundprobleme der Mathematischen Theorie Elektromagnetischer Schwingungen
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Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie I
| SKU | Unavailable |
| ISBN 13 | 9783642859915 |
| ISBN 10 | 3642859917 |
| Title | Continuous Transformations in Analysis |
| Author | Tibor Rado |
| Series | Grundlehren Der Mathematischen Wissenschaften |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2012-04-09 |
| Number of pages | 442 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |