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Two remarks on the Suita conjecture

Nikolai Nikolov (2015)

Annales Polonici Mathematici

It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with C 1 + ε -smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.

(Ultra)differentiable functional calculus and current extension of the resolvent mapping

Mats Andersson (2003)

Annales de l’institut Fourier

Let a = ( a 1 , ... , a n ) be a tuple of commuting operators on a Banach space X . We discuss various conditions equivalent to that the holomorphic (Taylor) functional calculus has an extension to the real-analytic functions or various ultradifferentiable classes. In particular, we discuss the possible existence of a functional calculus for smooth functions. We relate the existence of a possible extension to existence of a certain (ultra)current extension of the resolvent mapping over the (Taylor) spectrum of a . If a ...

Uniform estimates for the Cauchy-Riemann equation on q -convex wedges

Christine Laurent-Thiébaut, Jurgen Leiterer (1993)

Annales de l'institut Fourier

We study the -equation with Hölder estimates in q -convex wedges of n by means of integral formulas. If D n is defined by some inequalities { ρ i 0 } , where the real hypersurfaces { ρ i = 0 } are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the ρ i ’s have at least ( q + 1 ) positive eigenvalues, we solve the equation f = g for each continuous ( n , r ) -closed form g in D , n - q r n , with the following estimates: if d denotes the distance to the boundary of D and if d β g is bounded, then for all ϵ > 0 ,...

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