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Titlebook: Entire Functions of Several Complex Variables; Pierre Lelong,Lawrence Gruman Book 1986 Springer-Verlag Berlin Heidelberg 1986 Area.Complex

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書目名稱Entire Functions of Several Complex Variables
編輯Pierre Lelong,Lawrence Gruman
視頻videohttp://file.papertrans.cn/312/311647/311647.mp4
叢書名稱Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Entire Functions of Several Complex Variables;  Pierre Lelong,Lawrence Gruman Book 1986 Springer-Verlag Berlin Heidelberg 1986 Area.Complex
描述I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen- dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp- totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions dem
出版日期Book 1986
關(guān)鍵詞Area; Complex analysis; Frechet Spaces; Functions; Lelong; Schwarz lemma; Variables; analytic number theory
版次1
doihttps://doi.org/10.1007/978-3-642-70344-7
isbn_softcover978-3-642-70346-1
isbn_ebook978-3-642-70344-7Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1986
The information of publication is updating

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The Relationship Between the Growth of an Entire Function and the Growth of its Zero Set,enth century. He showed that if . is a domain in the complex plane, if {.} is a sequence of points without limit point in ., and if {.} is a sequence of positive integers, then there exists a function .(.)∈ ?(.) which has a zero of order exactly . at every point .. The equivalent problem for several
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Convolution Operators on Linear Spaces of Entire Functions,equence of Cauchy’s Theorem in the polydisc, for instance, that this includes all finite order differential operators with constant coefficients, and if we choose ., δ the Dirac measure, then we obtain the finite difference operator ..
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Local Metric Properties of Zero Sets and Positive Closed Currents,and hence an orientation. This led to the introduction of a positive differential form in the exterior differential algebra E.(.) with involution (given by .→.) and its generalization, the positive closed current.
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Functions of Regular Growth,tically if and only if it has “regular growth” asymptotically along all rays. An equivalent formulation, as we shall see, is to say that for an entire function ., . log ∣. (.)∣ converges (as a distribution) in .(?.) to h.(.) if and only if .log ∣ .(.)∣ converges as a distribution to .(.). These ideas of regularity will be made more precise below.
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