Книга "i-Smooth Analysis" представляет собой новое направление в математике, которое изучает теорию и применение инвариантных производных функций и функционалов. В книге вводится новый класс инвариантных производных и показываются их связи с другими производными, такими как обобщенная производная Соболева и обобщенная производная теории распределений. До сих пор i-гладкий анализ развивался главным образом для применения к теории функционально-дифференциальных уравнений, и цель этой книги - представить i-гладкий анализ как ветвь функционального анализа. В книге также вводится понятие инвариантной производной для нелинейных функционалов, развивается соответствующий i-гладкий исчислений функционалов и показывается, что для линейных непрерывных функционалов инвариантная производная совпадает с обобщенной производной теории распределений. Книга рассчитана на математиков, инженеров и физиков, которые интересуются этой новой областью математики.
The edition introduces a novel class of invariant differential operators and examines their ties to other such operators, namely the Sobolev ones, as well as those from distribution theory. These newcomer directions provide scientifically novel inference avenues. I-Smooth theory is the section of functional theory that concerns the study of the relevant operations of transformation of functions and also multidimensional variables. And it enlists the key viewpoint of invariant operators' interactions with the aforementioned Sobolev operators and likewise, the overall operators from distributional theory. In reality, the i-diffusion theory most often holds true via the consideration of the pertinent spheres of interest in functional differential diagrams; the guiding aim of such a volume is to place the said study firmly classified within the veritable range of the holistic subject of functional theory. A header for the anomalous interpretation of abnormal cutaneous expressions has lately been put forward in mathematical studies, with the consequence-focused invariant operator (i-operator) being introduced, inspiring the ensuing curvilinear i-calculus of differential expressions. For independent multi-legged functions, inveterate theories demonstrate that the abnormal operators are identical to the overwhelmingly touted theoretical zero-potentialization. However, to believe is anything but true for strongly linear, continuous late functions. This information-rich tract decrees to weave these notions into the fabric of endogenous education.
Электронная Книга «i-Smooth Analysis» написана автором A. V. Kim в году.
Минимальный возраст читателя: 0
Язык: Английский
ISBN: 9781118998526
Описание книги от A. V. Kim
The edition introduces a new class of invariant derivatives and shows their relationships with other derivatives, such as the Sobolev generalized derivative and the generalized derivative of the distribution theory. This is a new direction in mathematics. i-Smooth analysis is the branch of functional analysis that considers the theory and applications of the invariant derivatives of functions and functionals. The important direction of i-smooth analysis is the investigation of the relation of invariant derivatives with the Sobolev generalized derivative and the generalized derivative of distribution theory. Until now, i-smooth analysis has been developed mainly to apply to the theory of functional differential equations, and the goal of this book is to present i-smooth analysis as a branch of functional analysis. The notion of the invariant derivative (i-derivative) of nonlinear functionals has been introduced in mathematics, and this in turn developed the corresponding i-smooth calculus of functionals and showed that for linear continuous functionals the invariant derivative coincides with the generalized derivative of the distribution theory. This book intends to introduce this theory to the general mathematics, engineering, and physicist communities.
