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  • 1
    Book
    Book
    Pseudodifferential and singular integral operators : an introduction with applications (2012)
    Berlin [u.a.] :De Gruyter,
    Details
    UID:
    almafu_BV039557727
    Format: X, 222 S. : , graph. Darst.
    ISBN: 978-3-11-025030-5
    Series Statement: De Gruyter graduate lectures
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-3-11-025031-2
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    Keywords: Pseudodifferentialoperator ; Singulärer Integraloperator
    URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409474&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
    URL: Inhaltsverzeichnis
    URL: Inhaltstext
    URL: Inhaltstext
    URL: Cover
    URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409474&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
    URL: Inhaltsverzeichnis
    Author information: Abels, Helmut 1975-
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  • 2
    Online Resource
    Online Resource
    Pseudodifferential and singular integral operators : an introduction with applications. (2012)
    Berlin [u.a.] :De Gruyter,
    Details
    UID:
    almafu_BV042348143
    Format: 1 Online-Ressource (X, 222 S.) : , graph. Darst.
    ISBN: 978-3-11-025031-2
    Series Statement: De Gruyter Textbook
    Note: Description based upon print version of record. - Helmut Abels. - This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. It presents the necessary material on Fourier transformation and distribution theory, the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space, an introduction to the theory of singular integral operators, the modern theory of Besov and Bessel potential spaces, and several applications to wellposedness and regularity question for elliptic and parabolic equations. The basic notation of fu
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-11-025030-5
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    Keywords: Pseudodifferentialoperator ; Singulärer Integraloperator
    DOI: 10.1515/9783110250312
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext  (lizenzpflichtig)
    URL: lizenzpflichtig
    URL: Cover
    URL: Inhaltstext
    URL: Cover
    URL: https://doi.org/10.1515/9783110250312
    URL: https://doi.org/10.1515/9783110250312
    URL: https://www.degruyter.com/isbn/9783110250312
    URL: Cover
    URL: https://doi.org/10.1515/9783110250312
    URL: https://www.degruyter.com/isbn/9783110250312
    URL: Cover
    Author information: Abels, Helmut 1975-
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Online Access
    Open Access Request
    HU Berlin
    FU Berlin
    UB Potsdam
  • 3
    Online Resource
    Online Resource
    Pseudodifferential and Singular Integral Operators : An Introduction with Applications (2011)
    [s.l.] : Walter de Gruyter GmbH Co.KG
    Details
    UID:
    almahu_9947359992502882
    Format: Online-Ressource , Online Ressource (222 S.)
    Edition: 1. Aufl.
    ISBN: 3110250306
    Content: Helmut Abels
    Content: This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. It presents the necessary material on Fourier transformation and distribution theory, the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space, an introduction to the theory of singular integral operators, the modern theory of Besov and Bessel potential spaces, and several applications to wellposedness and regularity question for elliptic and parabolic equations. The basic notation of fu
    Note: Description based upon print version of record , 2.9.2 Exercises3 Basic Calculus of Pseudodifferential Operators on Rn; 3.1 Symbol Classes and Basic Properties; 3.2 Composition of Pseudodifferential Operators: Motivation; 3.3 Oscillatory Integrals; 3.4 Double Symbols; 3.5 Composition of Pseudodifferential Operators; 3.6 Application: Elliptic Pseudodifferential Operators and Parametrices; 3.7 Boundedness on Cb8 (Rn) and Uniqueness of the Symbol; 3.8 Adjoints of Pseudodifferential Operators and Operators in (x, y )-Form; 3.9 Boundedness on L2(Rn) and L2-Bessel Potential Spaces; 3.10 Outlook: Coordinate Transformations and PsDOs on Manifolds. , 3.11 Final Remarks and Exercises3.11.1 Further Reading; 3.11.2 Exercises; II Singular Integral Operators; 4 Translation Invariant Singular Integral Operators; 4.1 Motivation; 4.2 Main Result in the Translation Invariant Case; 4.3 Calderón-Zygmund Decomposition and the Maximal Operator; 4.4 Proof of the Main Result in the Translation Invariant Case; 4.5 Examples of Singular Integral Operators; 4.6 Mikhlin Multiplier Theorem; 4.7 Outlook: Hardy spaces and BMO; 4.8 Final Remarks and Exercises; 4.8.1 Further Reading; 4.8.2 Exercises; 5 Non-Translation Invariant Singular Integral Operators. , 5.1 Motivation5.2 Extension to Non-Translation Invariant and Vector-Valued Singular Integral Operators; 5.3 Hilbert-Space-Valued Mikhlin Multiplier Theorem; 5.4 Kernel Representation of a Pseudodifferential Operator; 5.5 Consequences of the Kernel Representation; 5.6 Final Remarks and Exercises; 5.6.1 Further Reading; 5.6.2 Exercises; III Applications to Function Space and Differential Equations; 6 Introduction to Besov and Bessel Potential Spaces; 6.1 Motivation; 6.2 A Fourier-Analytic Characterization of Holder Continuity. , 6.3 Bessel Potential and Besov Spaces - Definitions and Basic Properties6.4 Sobolev Embeddings; 6.5 Equivalent Norms; 6.6 Pseudodifferential Operators on Besov Spaces; 6.7 Final Remarks and Exercises; 6.7.1 Further Reading; 6.7.2 Exercises; 7 Applications to Elliptic and Parabolic Equations; 7.1 Applications of the Mikhlin Multiplier Theorem; 7.1.1 Resolvent of the Laplace Operator; 7.1.2 Spectrum of Multiplier Operators with Homogeneous Symbols; 7.1.3 Spectrum of a Constant Coefficient Differential Operator; 7.2 Applications of the Hilbert-Space-Valued Mikhlin Multiplier Theorem. , 7.2.1 Maximal Regularity of Abstract ODEs in Hilbert Spaces. , Preface; 1 Introduction; I Fourier Transformation and Pseudodifferential Operators; 2 Fourier Transformation and Tempered Distributions; 2.1 Definition and Basic Properties; 2.2 Rapidly Decreasing Functions - P (Rn); 2.3 Inverse Fourier Transformation and Plancherel's Theorem; 2.4 Tempered Distributions and Fourier Transformation; 2.5 Fourier Transformation and Convolution of Tempered Distributions; 2.6 Convolution on on P'(Rn) and Fundamental Solutions; 2.7 Sobolev and Bessel Potential Spaces; 2.8 Vector-Valued Fourier-Transformation; 2.9 Final Remarks and Exercises; 2.9.1 Further Reading.
    Additional Edition: ISBN 3110250314
    Additional Edition: ISBN 9783110250312
    Language: English
    Keywords: Electronic books
    DOI: 10.1515/9783110250312
    URL: http://www.degruyter.com/doi/book/10.1515/9783110250312
    URL: Cover
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  • 4
    Online Resource
    Online Resource
    Pseudodifferential and Singular Integral Operators : An Introduction with Applications (2011)
    Berlin ;Boston :De Gruyter,
    Details
    UID:
    edocfu_9958353809702883
    Format: 1 online resource (232p.)
    ISBN: 9783110250312
    Series Statement: De Gruyter Textbook
    Content: This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.
    Note: Frontmatter -- , Preface -- , Contents -- , Chapter. 1 Introduction -- , Part I. Fourier Transformation and Pseudodifferential Operators -- , Chapter 2. Fourier Transformation and Tempered Distributions -- , Chapter 3. Basic Calculus of Pseudodifferential Operators on ℝn -- , Part II. Singular Integral Operators -- , Chapter 4. Translation Invariant Singular Integral Operators -- , Chapter 5. Non-Translation Invariant Singular Integral Operators -- , Part III. Applications to Function Space and Differential Equations -- , Chapter 6. Introduction to Besov and Bessel Potential Spaces -- , Chapter 7. Applications to Elliptic and Parabolic Equations -- , Part IV. Appendix -- , Appendix A Basic Results from Analysis -- , Bibliography -- , Index , In English.
    Language: English
    DOI: 10.1515/9783110250312
    URL: https://doi.org/10.1515/9783110250312
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
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    FU Berlin
  • 5
    Online Resource
    Online Resource
    Pseudodifferential and singular integral operators : an introduction with applications. (2012)
    Berlin [u.a.] :De Gruyter,
    Details
    UID:
    edocfu_BV042348143
    Format: 1 Online-Ressource (X, 222 S.) : , graph. Darst.
    ISBN: 978-3-11-025031-2
    Series Statement: De Gruyter Textbook
    Note: Description based upon print version of record. - Helmut Abels. - This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. It presents the necessary material on Fourier transformation and distribution theory, the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space, an introduction to the theory of singular integral operators, the modern theory of Besov and Bessel potential spaces, and several applications to wellposedness and regularity question for elliptic and parabolic equations. The basic notation of fu
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-11-025030-5
    Language: English
    Keywords: Pseudodifferentialoperator ; Singulärer Integraloperator
    DOI: 10.1515/9783110250312
    URL: Volltext  (URL des Erstveröffentlichers)
    Author information: Abels, Helmut 1975-
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Online Resource
    Online Access
    Open Access Request
    FU Berlin
  • 6
    Online Resource
    Online Resource
    Pseudodifferential and singular integral operators : an introduction with applications (2012)
    Berlin :De Gruyter,
    Details
    UID:
    almafu_9959242573002883
    Format: 1 online resource (232 p.)
    Edition: 1st ed.
    ISBN: 3-11-025031-4
    Series Statement: De Gruyter graduate lectures
    Content: This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.
    Note: Description based upon print version of record. , pt. 1. Fourier transformation and pseudodifferential operators -- pt. 2. Singular integral operators -- pt. 3. Applications to function space and differential equations -- pt. 4. Appendix. , English
    Additional Edition: ISBN 3-11-025030-6
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    DOI: 10.1515/9783110250312
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    FU Berlin
  • 7
    Online Resource
    Online Resource
    Pseudodifferential and Singular Integral Operators : An Introduction with Applications (2011)
    Berlin ; : De Gruyter,
    Details
    UID:
    almahu_9949481307802882
    Format: 1 online resource (222 p.)
    ISBN: 9783110250312 , 9783110238570
    Series Statement: De Gruyter Textbook
    Content: This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.
    Note: Frontmatter -- , Preface -- , Contents -- , Chapter. 1 Introduction -- , Part I. Fourier Transformation and Pseudodifferential Operators -- , Chapter 2. Fourier Transformation and Tempered Distributions -- , Chapter 3. Basic Calculus of Pseudodifferential Operators on ℝn -- , Part II. Singular Integral Operators -- , Chapter 4. Translation Invariant Singular Integral Operators -- , Chapter 5. Non-Translation Invariant Singular Integral Operators -- , Part III. Applications to Function Space and Differential Equations -- , Chapter 6. Introduction to Besov and Bessel Potential Spaces -- , Chapter 7. Applications to Elliptic and Parabolic Equations -- , Part IV. Appendix -- , Appendix A Basic Results from Analysis -- , Bibliography -- , Index , Mode of access: Internet via World Wide Web. , In English.
    In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
    In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
    In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
    In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011, De Gruyter, 9783110261189
    In: E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011, De Gruyter, 9783110261233
    In: E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011, De Gruyter, 9783110261202
    Additional Edition: ISBN 9783110250305
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    DOI: 10.1515/9783110250312
    URL: https://doi.org/10.1515/9783110250312
    URL: https://www.degruyter.com/isbn/9783110250312
    URL: Cover
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    HU Berlin
  • 8
    Online Resource
    Online Resource
    Pseudodifferential and Singular Integral Operators : An Introduction with Applications (2011)
    Berlin ; : De Gruyter,
    Details
    UID:
    almahu_9949462115002882
    Format: 1 online resource (222 p.)
    ISBN: 9783110250312 , 9783110238570
    Series Statement: De Gruyter Textbook
    Content: This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.
    Note: Frontmatter -- , Preface -- , Contents -- , Chapter. 1 Introduction -- , Part I. Fourier Transformation and Pseudodifferential Operators -- , Chapter 2. Fourier Transformation and Tempered Distributions -- , Chapter 3. Basic Calculus of Pseudodifferential Operators on ℝn -- , Part II. Singular Integral Operators -- , Chapter 4. Translation Invariant Singular Integral Operators -- , Chapter 5. Non-Translation Invariant Singular Integral Operators -- , Part III. Applications to Function Space and Differential Equations -- , Chapter 6. Introduction to Besov and Bessel Potential Spaces -- , Chapter 7. Applications to Elliptic and Parabolic Equations -- , Part IV. Appendix -- , Appendix A Basic Results from Analysis -- , Bibliography -- , Index , Mode of access: Internet via World Wide Web. , In English.
    In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
    In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
    In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
    In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011, De Gruyter, 9783110261189
    In: E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011, De Gruyter, 9783110261233
    In: E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011, De Gruyter, 9783110261202
    Additional Edition: ISBN 9783110250305
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    DOI: 10.1515/9783110250312
    URL: https://doi.org/10.1515/9783110250312
    URL: https://www.degruyter.com/isbn/9783110250312
    URL: Cover
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Online Resource
    Open Access Request
    HU Berlin
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