Verfügbarkeit: Bicomplex holomorphic functions | Technische Universität München

Bicomplex holomorphic functions: the algebra, geometry and analysis of bicomplex numbers

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Beteiligte Personen:	Luna-Elizarrarás, M. Elena (VerfasserIn), Shapiro, Michael 1963- (VerfasserIn), Struppa, Daniele Carlo 1955- (VerfasserIn), Vajiac, Adrian (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	Englisch
Veröffentlicht:	[Basel] Birkhäuser [2015] Cham Springer [2015]
Schriftenreihe:	Frontiers in mathematics
Schlagwörter:	Mathematics Functions of complex variables Mathematical physics Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematical Applications in the Physical Sciences Mathematik Mathematische Physik
Links:	https://doi.org/10.1007/978-3-319-24868-4 https://doi.org/10.1007/978-3-319-24868-4 https://doi.org/10.1007/978-3-319-24868-4 https://doi.org/10.1007/978-3-319-24868-4 https://doi.org/10.1007/978-3-319-24868-4 https://doi.org/10.1007/978-3-319-24868-4 https://doi.org/10.1007/978-3-319-24868-4 https://doi.org/10.1007/978-3-319-24868-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730390&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730390&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	1 Online Ressource (VIII, 231 Seiten, 23 illus)
ISBN:	9783319248684
ISSN:	1660-8046
DOI:	10.1007/978-3-319-24868-4

Internformat

MARC


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Datensatz im Suchindex

DE-BY-TUM_katkey	2165940
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adam_text	BICOMPLEX HOLOMORPHIC FUNCTIONS / LUNA-ELIZARRARAS, M. ELENA : 2015 TABLE OF CONTENTS / INHALTSVERZEICHNIS INTRODUCTION 1.THE BICOMPLEX NUMBERS 2.ALGEBRAIC STRUCTURES OF THE SET OF BICOMPLEX NUMBERS 3.GEOMETRY AND TRIGONOMETRIC REPRESENTATIONS OF BICOMPLEX 4.LINES AND CURVES IN BC 5.LIMITS AND CONTINUITY 6.ELEMENTARY BICOMPLEX FUNCTIONS 7.BICOMPLEX DERIVABILITY AND DIFFERENTIABILITY 8.SOME PROPERTIES OF BICOMPLEX HOLOMORPHIC FUNCTIONS 9.SECOND ORDER COMPLEX AND HYPERBOLIC DIFFERENTIAL OPERATORS 10.SEQUENCES AND SERIES OF BICOMPLEX FUNCTIONS 11.INTEGRAL FORMULAS AND THEOREMS BIBLIOGRAPHY DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. BICOMPLEX HOLOMORPHIC FUNCTIONS / LUNA-ELIZARRARAS, M. ELENA : 2015 ABSTRACT / INHALTSTEXT THE PURPOSE OF THIS BOOK IS TO DEVELOP THE FOUNDATIONS OF THE THEORY OF HOLOMORPHICITY ON THE RING OF BICOMPLEX NUMBERS. ACCORDINGLY, THE MAIN FOCUS IS ON EXPRESSING THE SIMILARITIES WITH, AND DIFFERENCES FROM, THE CLASSICAL THEORY OF ONE COMPLEX VARIABLE. THE RESULT IS AN ELEMENTARY YET COMPREHENSIVE INTRODUCTION TO THE ALGEBRA, GEOMETRY AND ANALYSIS OF BICOMPLEX NUMBERS. AROUND THE MIDDLE OF THE NINETEENTH CENTURY, SEVERAL MATHEMATICIANS (THE BEST KNOWN BEING SIR WILLIAM HAMILTON AND ARTHUR CAYLEY) BECAME INTERESTED IN STUDYING NUMBER SYSTEMS THAT EXTENDED THE FIELD OF COMPLEX NUMBERS. HAMILTON FAMOUSLY INTRODUCED THE QUATERNIONS, A SKEW FIELD IN REAL-DIMENSION FOUR, WHILE ALMOST SIMULTANEOUSLY JAMES COCKLE INTRODUCED A COMMUTATIVE FOUR-DIMENSIONAL REAL ALGEBRA, WHICH WAS REDISCOVERED IN 1892 BY CORRADO SEGRE, WHO REFERRED TO HIS ELEMENTS AS BICOMPLEX NUMBERS. THE ADVANTAGES OF COMMUTATIVITY WERE ACCOMPANIED BY THE INTRODUCTION OF ZERO DIVISORS, SOMETHING THAT FOR A WHILE DAMPENED INTEREST IN THIS SUBJECT. IN RECENT YEARS, DUE LARGELY TO THE WORK OF G.B. PRICE, THERE HAS BEEN A RESURGENCE OF INTEREST IN THE STUDY OF THESE NUMBERS AND, MORE IMPORTANTLY, IN THE STUDY OF FUNCTIONS DEFINED ON THE RING OF BICOMPLEX NUMBERS, WHICH MIMIC THE BEHAVIOR OF HOLOMORPHIC FUNCTIONS OF A COMPLEX VARIABLE. WHILE THE ALGEBRA OF BICOMPLEX NUMBERS IS A FOUR-DIMENSIONAL REAL ALGEBRA, IT IS USEFUL TO THINK OF IT AS A “COMPLEXIFICATION” OF THE FIELD OF COMPLEX NUMBERS; FROM THIS PERSPECTIVE, THE BICOMPLEX ALGEBRA POSSESSES THE PROPERTIES OF A ONE-DIMENSIONAL THEORY INSIDE FOUR REAL DIMENSIONS. ITS RICH ANALYSIS AND INNOVATIVE GEOMETRY PROVIDE NEW IDEAS AND POTENTIAL APPLICATIONS IN RELATIVITY AND QUANTUM MECHANICS ALIKE. THE BOOK WILL APPEAL TO RESEARCHERS IN THE FIELDS OF COMPLEX, HYPERCOMPLEX AND FUNCTIONAL ANALYSIS, AS WELL AS UNDERGRADUATE AND GRADUATE STUDENTS WITH AN INTEREST IN ONE- OR MULTIDIMENSIONAL COMPLEX ANALYSIS DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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author	Luna-Elizarrarás, M. Elena Shapiro, Michael 1963- Struppa, Daniele Carlo 1955- Vajiac, Adrian
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series2	Frontiers in mathematics
spellingShingle	Luna-Elizarrarás, M. Elena Shapiro, Michael 1963- Struppa, Daniele Carlo 1955- Vajiac, Adrian Bicomplex holomorphic functions the algebra, geometry and analysis of bicomplex numbers Mathematics Functions of complex variables Mathematical physics Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematical Applications in the Physical Sciences Mathematik Mathematische Physik
title	Bicomplex holomorphic functions the algebra, geometry and analysis of bicomplex numbers
title_auth	Bicomplex holomorphic functions the algebra, geometry and analysis of bicomplex numbers
title_exact_search	Bicomplex holomorphic functions the algebra, geometry and analysis of bicomplex numbers
title_full	Bicomplex holomorphic functions the algebra, geometry and analysis of bicomplex numbers M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac
title_fullStr	Bicomplex holomorphic functions the algebra, geometry and analysis of bicomplex numbers M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac
title_full_unstemmed	Bicomplex holomorphic functions the algebra, geometry and analysis of bicomplex numbers M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac
title_short	Bicomplex holomorphic functions
title_sort	bicomplex holomorphic functions the algebra geometry and analysis of bicomplex numbers
title_sub	the algebra, geometry and analysis of bicomplex numbers
topic	Mathematics Functions of complex variables Mathematical physics Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematical Applications in the Physical Sciences Mathematik Mathematische Physik
topic_facet	Mathematics Functions of complex variables Mathematical physics Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematical Applications in the Physical Sciences Mathematik Mathematische Physik
url	https://doi.org/10.1007/978-3-319-24868-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730390&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730390&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
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