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^k-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.--
- 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 Second-Order Leibniz rule
- Non-localization Results
- The Second-Order 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^k-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.--
- 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 Second-Order Leibniz rule -- Non-localization Results -- The Second-Order Chain Rule -- Bibliography -- Subject Index -- Author Index
- Control code
- 978-3-030-00241-1
- 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, non-commercial 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 Second-Order Leibniz rule -- Non-localization Results -- The Second-Order Chain Rule -- Bibliography -- Subject Index -- Author Index
- Control code
- 978-3-030-00241-1
- 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, non-commercial 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 fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.eui.eu/portal/Operator-Relations-Characterizing-Derivatives-by/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/Operator-Relations-Characterizing-Derivatives-by/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>