Titlebook: Holomorphic Operator Functions of One Variable and Applications; Methods from Complex Israel Gohberg,Jürgen Leiterer Book 2009 Birkhäuser B

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书目名称Holomorphic Operator Functions of One Variable and Applications影响因子(影响力)




书目名称Holomorphic Operator Functions of One Variable and Applications影响因子(影响力)学科排名




书目名称Holomorphic Operator Functions of One Variable and Applications网络公开度




书目名称Holomorphic Operator Functions of One Variable and Applications网络公开度学科排名




书目名称Holomorphic Operator Functions of One Variable and Applications被引频次




书目名称Holomorphic Operator Functions of One Variable and Applications被引频次学科排名




书目名称Holomorphic Operator Functions of One Variable and Applications年度引用




书目名称Holomorphic Operator Functions of One Variable and Applications年度引用学科排名




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书目名称Holomorphic Operator Functions of One Variable and Applications读者反馈学科排名

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Elementary properties of holomorphic functions,This chapter is devoted to the basic facts usually contained in a basic course on Complex analysis of one variable. The difference is that we do this for functions with values in a Banach space. Many (not all) of these results will be deduced by the Hahn-Banach theorem from the corresponding scalar fact.

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Solution of , and applications,In complex analysis of several variables, the inhomogeneous Cauchy-Riemann equation is an important tool. For results in Complex analysis of one variable this equation is also important, but it is missing in many standard books.

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,The Rouché theorem for operator functions,In this chapter we generalize to finite meromorphic Fredholm operator functions the classical Rouché theorem from Complex analysis and the Smith factorization form. The proof is based on the local Smith form for matrix functions.

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Multiplicative cocycles (,-cocycles),Let . be a Banach algebra with unit 1, and let . be an open subgroup of the group of invertible elements of .. The Runge approximation Theorem 2.5.6 for invertible scalar functions admits the following generalization:

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Families of subspaces,Let . be a Banach space. We denote by . the set of closed subspaces of .. In this chapter we study functions with values in ..

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Multiplicative cocycles with restrictions (,-cocycles),Here we present a generalization of the theory of cocycles developed in Chapter 5. We study multiplicative cocycles with .. To formulate this, it is convenient to use the language of sheaves.