Displaying similar documents to “Modular invariant theory and the iterated total power operation”

Composition operators on Banach spaces of formal power series

B. Yousefi, S. Jahedi (2003)

Bollettino dell'Unione Matematica Italiana

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Let β ⁢ n n = 0 ∞ be a sequence of positive numbers and 1 ≤ p < ∞ . We consider the space H p ⁢ β of all power series f ⁢ z = ∑ n = 0 ∞ f ⌃ ⁢ n ⁢ z n such that ∑ n = 0 ∞ f ⌃ ⁢ n p ⁢ β ⁢ n p < ∞ . Suppose that 1 p + 1 q = 1 and ∑ n = 1 ∞ n q ⁢ j β ⁢ n q = ∞ for some nonnegative integer j . We show that if C φ is compact on H p ⁢ β , then the non-tangential limit of φ j + 1 has modulus greater than one at each boundary point of the open unit disc. Also we show that if C φ is Fredholm on H p ⁢ β , then φ must be an automorphism of the open unit disc.

On the range of elliptic operators discontinuous at one point

Cristina Giannotti (2002)

Bollettino dell'Unione Matematica Italiana

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Let L be a second order, uniformly elliptic, non variational operator with coefficients which are bounded and measurable in R d ( d ≥ 3 ) and continuous in R d ∖ 0 . Then, if Ω ⊂ R d is a bounded domain, we prove that L ⁢ W 2 , p ⁢ Ω is dense in L p ⁢ Ω for any p ∈ 1 , d / 2 .