Displaying similar documents to “Removable singularities for H p spaces of analytic functions, 0 < p < 1 .”

Removable singularities for weighted Bergman spaces

Anders Björn (2006)

Czechoslovak Mathematical Journal

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We develop a theory of removable singularities for the weighted Bergman space 𝒜 μ p ( Ω ) = { f analytic in Ω ∫ Ω | f | p d μ < ∞ } , where μ is a Radon measure on ℂ . The set A is weakly removable for 𝒜 μ p ( Ω ∖ A ) if 𝒜 μ p ( Ω ∖ A ) ⊂ Hol ( Ω ) , and strongly removable for 𝒜 μ p ( Ω ∖ A ) if 𝒜 μ p ( Ω ∖ A ) = 𝒜 μ p ( Ω ) . The general theory developed is in many ways similar to the theory of removable singularities for Hardy H p spaces, B M O and locally Lipschitz spaces of analytic functions, including the existence of counterexamples to many plausible properties, e.g. the union of two compact removable singularities needs...

Topological K-equivalence of analytic function-germs

Sérgio Alvarez, Lev Birbrair, João Costa, Alexandre Fernandes (2010)

Open Mathematics

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We study the topological K-equivalence of function-germs (ℝn, 0) → (ℝ, 0). We present some special classes of piece-wise linear functions and prove that they are normal forms for equivalence classes with respect to topological K-equivalence for definable functions-germs. For the case n = 2 we present polynomial models for analytic function-germs.