03283nam 22005415i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001200172072001700184072002300201082001500224100003100239245007100270264004600341300003200387336002600419337002600445338003600471347002400507490003500531505021600566520132400782650001702106650001302123650002802136650002702164650002802191650002502219650003602244650001702280650005102297650003702348650003402385650002502419650001402444710003402458773002002492776003602512830003502548856004802583912001402631999001902645952007702664978-0-8176-4538-0DE-He21320180115171434.0cr nn 008mamaa100301s2007 xxu| s |||| 0|eng d a97808176453809978-0-8176-4538-07 a10.1007/978-0-8176-4538-02doi 4aQA331.7 7aPBKD2bicssc 7aMAT0340002bisacsh04a515.942231 aStout, Edgar Lee.eauthor.10aPolynomial Convexityh[electronic resource] /cby Edgar Lee Stout. 1aBoston, MA :bBirkhèauser Boston,c2007. aX, 439 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aProgress in Mathematics ;v2610 aSome General Properties of Polynomially Convex Sets -- Sets of Finite Length -- Sets of Class A1 -- Further Results -- Approximation -- Varieties in Strictly Pseudoconvex Domains -- Examples and Counterexamples. aThis comprehensive monograph is devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables. Important features of Polynomial Convexity: *Presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. *Motivates the theory with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries. *Examines in considerable detail questions of uniform approximation, especially on totally real sets, for the most part on compact sets but with some attention to questions of global approximation on noncompact sets. *Discusses important applications, e.g., to the study of analytic varieties and to the theory of removable singularities for CR functions. *Requires of the reader a solid background in real and complex analysis together with some previous experience with the theory of functions of several complex variables as well as the elements of functional analysis. This beautiful exposition of a rich and complex theory, which contains much material not available in other texts, is destined to be the standard reference for many years, and will appeal to all those with an interest in multivariate complex analysis. 0aMathematics. 0aAlgebra. 0aField theory (Physics). 0aMathematical analysis. 0aAnalysis (Mathematics). 0aFunctional analysis. 0aFunctions of complex variables.14aMathematics.24aSeveral Complex Variables and Analytic Spaces.24aFunctions of a Complex Variable.24aField Theory and Polynomials.24aFunctional Analysis.24aAnalysis.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817645373 0aProgress in Mathematics ;v26140uhttp://dx.doi.org/10.1007/978-0-8176-4538-0 aZDB-2-SMA c369916d369916 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK