D`Oh! Fourier: Theory, Applications, and Derivatives, Nixon Mark S.

Автор: Hermann K?nig; Vitali Milman
Название: Operator Relations Characterizing Derivatives
ISBN: 3030002403 ISBN-13(EAN): 9783030002404
Издательство: Springer
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Цена: 6986.00 р.
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Описание: This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature. Major constructions or operations in analysis are often characterized by some elementary properties, relations or equations which they satisfy. The authors present recent results on the problem to what extent the derivative is characterized by equations such as the Leibniz rule or the Chain rule operator equation in Ck-spaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, Sturm-Liouville operators and the Laplacian motivate the study of certain 'second-order' operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of non-degeneration. In their approach, operators are not required to be linear, and the authors also try to avoid continuity conditions. The Leibniz rule, the Chain rule and its extensions turn out to be stable under perturbations and relaxations of assumptions on the form of the operators. The results yield an algebraic understanding of first- and second-order differential operators. Because the authors have chosen to characterize the derivative by algebraic relations, the rich operator-type structure behind the fundamental notion of the derivative and its relatives in analysis is discovered and explored.The book does not require any specific knowledge of functional equations. All needed results are presented and proven and the book is addressed to a general mathematical audience.

Автор: Dragoslav S. Mitrinovic; J. Pecaric; A.M Fink
Название: Inequalities Involving Functions and Their Integrals and Derivatives
ISBN: 0792313305 ISBN-13(EAN): 9780792313304
Издательство: Springer
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Цена: 18167.00 р.
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Описание: Provides a comprehensive survey of inequalities that involve a relationship between a function and its derivatives or integrals. This book is divided into 18 chapters dealing with specific inequalities such as those of Kolmogorov-Landau, Wirtinger, Hardy, Carlson, and others. It is for those involved in differential and integral equations.

Автор: George Isac; S?ndor Zolt?n N?meth
Название: Scalar and Asymptotic Scalar Derivatives
ISBN: 1441944842 ISBN-13(EAN): 9781441944849
Издательство: Springer
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Цена: 19564.00 р.
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Описание: This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds.

Автор: Benchohra
Название: Fractional Differential Equations
ISBN: 3031348761 ISBN-13(EAN): 9783031348761
Издательство: Springer
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Цена: 5589.00 р.
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Описание: This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.

Автор: Hermann K?nig; Vitali Milman
Название: Operator Relations Characterizing Derivatives
ISBN: 3030130967 ISBN-13(EAN): 9783030130961
Издательство: Springer
Рейтинг:
Цена: 11179.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature. Major constructions or operations in analysis are often characterized by some elementary properties, relations or equations which they satisfy. The authors present recent results on the problem to what extent the derivative is characterized by equations such as the Leibniz rule or the Chain rule operator equation in Ck-spaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, Sturm-Liouville operators and the Laplacian motivate the study of certain 'second-order' operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of non-degeneration. In their approach, operators are not required to be linear, and the authors also try to avoid continuity conditions. The Leibniz rule, the Chain rule and its extensions turn out to be stable under perturbations and relaxations of assumptions on the form of the operators. The results yield an algebraic understanding of first- and second-order differential operators. Because the authors have chosen to characterize the derivative by algebraic relations, the rich operator-type structure behind the fundamental notion of the derivative and its relatives in analysis is discovered and explored.The book does not require any specific knowledge of functional equations. All needed results are presented and proven and the book is addressed to a general mathematical audience.