Description

Book Synopsis
Uses as a starting point A B Aleksandrov's proof that nonconstant inner functions exist in the unit ball $B$ of $C^n$. This title simplifies the construction of such functions by using certain homogeneous polynomials discovered by Ryll and Wojtaszczyk; this yields solutions to a large number of problems.

Table of Contents
The pathology of inner functions $RW$-sequences Approximation by $E$-polynomials The existence of inner functions Radial limits and singular measures $E$-functions in the Smirnov class Almost semicontinuous functions and $\tilde{A}(B)$ $|u+vf|$ Approximation in $L^{1/2}$ The $L^1$-modification theorem Approximation by inner functions The LSC property of $H^\infty$ Max-sets and nonapproximation theorems Inner maps A Lusin-type theorem for $A(B)$ Continuity on open sets of full measure Composition with inner functions The closure of $A(B)$ in $(LH)^p(B)$ Open problems Appendix I. Bounded bases in $H^2(B)$ Appendix II. RW-sequences revisited References.

New Constructions of Functions Holomorphic in th Regional Conference

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    A Paperback by American Mathem American Mathem

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      View other formats and editions of New Constructions of Functions Holomorphic in th Regional Conference by American Mathem American Mathem

      Publisher: MP-AMM American Mathematical
      Publication Date: 30/12/1986
      ISBN13: 9780821807132, 978-0821807132
      ISBN10:

      Description

      Book Synopsis
      Uses as a starting point A B Aleksandrov's proof that nonconstant inner functions exist in the unit ball $B$ of $C^n$. This title simplifies the construction of such functions by using certain homogeneous polynomials discovered by Ryll and Wojtaszczyk; this yields solutions to a large number of problems.

      Table of Contents
      The pathology of inner functions $RW$-sequences Approximation by $E$-polynomials The existence of inner functions Radial limits and singular measures $E$-functions in the Smirnov class Almost semicontinuous functions and $\tilde{A}(B)$ $|u+vf|$ Approximation in $L^{1/2}$ The $L^1$-modification theorem Approximation by inner functions The LSC property of $H^\infty$ Max-sets and nonapproximation theorems Inner maps A Lusin-type theorem for $A(B)$ Continuity on open sets of full measure Composition with inner functions The closure of $A(B)$ in $(LH)^p(B)$ Open problems Appendix I. Bounded bases in $H^2(B)$ Appendix II. RW-sequences revisited References.

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