The Resource Operator Relations Characterizing Derivatives, by Hermann König, Vitali Milman, (electronic resource)
Operator Relations Characterizing Derivatives, by Hermann König, Vitali Milman, (electronic resource)
Resource Information
The item Operator Relations Characterizing Derivatives, by Hermann König, Vitali Milman, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Operator Relations Characterizing Derivatives, by Hermann König, Vitali Milman, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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 C^kspaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, SturmLiouville operators and the Laplacian motivate the study of certain "secondorder" operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of nondegeneration. 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 secondorder differential operators. Because the authors have chosen to characterize the derivative by algebraic relations, the rich operatortype 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.
 Language
 eng
 Extent
 1 online resource (VI, 191 pages)
 Contents

 Introduction
 Regular Solutions of Some Functional Equations
 The Leibniz Rule
 The Chain Rule
 Stability and Rigidity of the Leibniz and the Chain Rules
 The Chain Rule Inequality and its Perturbations
 The SecondOrder Leibniz rule
 Nonlocalization Results
 The SecondOrder Chain Rule
 Bibliography
 Subject Index
 Author Index
 Isbn
 9783030002411
 Label
 Operator Relations Characterizing Derivatives
 Title
 Operator Relations Characterizing Derivatives
 Statement of responsibility
 by Hermann König, Vitali Milman
 Language
 eng
 Summary
 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 C^kspaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, SturmLiouville operators and the Laplacian motivate the study of certain "secondorder" operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of nondegeneration. 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 secondorder differential operators. Because the authors have chosen to characterize the derivative by algebraic relations, the rich operatortype 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.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 König, Hermann
 Dewey number
 515.625
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Milman, Vitali
 Series statement

 Springer eBooks
 Springer eBooks.
 http://library.link/vocab/subjectName

 Functional equations
 Operator theory
 Mathematics
 Label
 Operator Relations Characterizing Derivatives, by Hermann König, Vitali Milman, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Regular Solutions of Some Functional Equations  The Leibniz Rule  The Chain Rule  Stability and Rigidity of the Leibniz and the Chain Rules  The Chain Rule Inequality and its Perturbations  The SecondOrder Leibniz rule  Nonlocalization Results  The SecondOrder Chain Rule  Bibliography  Subject Index  Author Index
 Control code
 9783030002411
 Dimensions
 unknown
 Extent
 1 online resource (VI, 191 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783030002411
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1056908463
 Label
 Operator Relations Characterizing Derivatives, by Hermann König, Vitali Milman, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Regular Solutions of Some Functional Equations  The Leibniz Rule  The Chain Rule  Stability and Rigidity of the Leibniz and the Chain Rules  The Chain Rule Inequality and its Perturbations  The SecondOrder Leibniz rule  Nonlocalization Results  The SecondOrder Chain Rule  Bibliography  Subject Index  Author Index
 Control code
 9783030002411
 Dimensions
 unknown
 Extent
 1 online resource (VI, 191 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783030002411
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1056908463
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/OperatorRelationsCharacterizingDerivativesby/DkQYu3oF8wA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/OperatorRelationsCharacterizingDerivativesby/DkQYu3oF8wA/">Operator Relations Characterizing Derivatives, by Hermann König, Vitali Milman, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>