Ideals in Rings of Analytic Functions with Smooth Boundary Values

  title={Ideals in Rings of Analytic Functions with Smooth Boundary Values},
  author={B. A. Taylor and D. L. Williams},
  journal={Canadian Journal of Mathematics},
  pages={1266 - 1283}
Let A denote the Banach algebra of functions analytic in the open unit disc D and continuous in . If f and its first m derivatives belong to A, then the boundary function f(eiθ) belongs to Cm(∂D). The space Am of all such functions is a Banach algebra with the topology induced by Cm(∂D). If all the derivatives of/ belong to A, then the boundary function belongs to C∞(∂D), and the space A∞ all such functions is a topological algebra with the topology induced by C∞(∂D). In this paper we determine… 
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The Closed Ideals in an Algebra of Analytic Functions
  • W. Rudin
  • Mathematics
    Canadian Journal of Mathematics
  • 1957
Let K and C be the closure and boundary, respectively, of the open unit disc U in the complex plane. Let be the Banach algebra whose elements are those continuous complex functions on K which are
Zeros of analytic functions with infinitely differentiable boundary values
A necessary and sufficient condition is proved that a set of points I r,ein } in the unit disk be the set of zeros of an analytic function with infinitely differentiable boundary values for every
On the "Edge of the Wedge" Theorem
  • F. Browder
  • Mathematics
    Canadian Journal of Mathematics
  • 1963
In the mathematical justification of the formal calculations of axiomatic quantum field theory and the theory of dispersion relations, a strategic role is played by a theorem on analytic functions of
On the existence of a largest subharmonic minorant of a given function
Gurariï, The structure of primary ideals in the rings of functions integrable with increasing weight on the half axis
  • Soviet Math. Dokl
  • 1968
Sets of uniqueness for functions regular in the unit circle
the classical result being that of Fatou. However, very little is known about the properties of this boundary function F (0), and in particular about the sets E associated with the class C, having
It is possible to avoid the appeal to Beurling's theorem by studying the structure of T(z) in more detail. Proof of Theorem 5.3. Let I be a closed ideal in ^4 ra and let I 0 = S •
  • Let J =
Let giz) = f(z)(z -a)-n~K By Proposition 4.5, g G ^4°°. For h £ I we have, again by Proposition 4.5, A(z) = (z -a) n+1 H(z), where ff G ,4 oe . Hence gh = fH £ I
  • ^4°°