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$μ$ -constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms of the Milnor lattice which respect not only the intersection form, but also the Seifert form and the monodromy. We conjecture that it contains all such automorphisms, modulo $\pm id$ . Second, marked singularities are defined and global moduli spaces for right equivalence...

$ω$ –weighted holomorphic Besov spaces on the unit ball in $C^{n}$

A. V. Harutyunyan, Wolfgang Lusky (2011)

Commentationes Mathematicae Universitatis Carolinae

The $ω$ -weighted Besov spaces of holomorphic functions on the unit ball $B^{n}$ in $C^{n}$ are introduced as follows. Given a function $ω$ of regular variation and $0 < p < \infty$ , a function $f$ holomorphic in $B^{n}$ is said to belong to the Besov space $B_{p} (ω)$ if ${∥ f ∥}_{B_{p} (ω)}^{p} = \int_{B^{n}} {(1 - | z |}^{2})^{p} {| D f (z) |}^{p} \frac{ω (1 - | z |)}{{(1 - | z |}^{2})^{n + 1}} d ν (z) < + \infty,$ where $d ν (z)$ is the volume measure on $B^{n}$ and $D$ stands for the fractional derivative of $f$ . The holomorphic Besov space is described in the terms of the corresponding $L_{p} (ω)$ space. Some projection theorems and theorems on existence of the inversions of these projections are proved. Also,...

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

Le Mau Hai, Nguyen Van Khue, Pham Hoang Hiep (2007)

Annales Polonici Mathematici

We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.

Алгебра непрерывных на сфере аналитических функций с совершенным множеством особенностей, и полиномиальная аппроксимация на толстых компактах в $ℂ^{n}$

В.Н. Сеничкин (1972)

Zapiski naucnych seminarov Leningradskogo

Аналитические свойства эйлеровых произведений для конгруэнц-подгрупп $S p_{2} (ℤ)$

С.А. Евдокимов (1979)

Matematiceskij sbornik

Аналитическое представление CR-функций

Е.М. Чирка (1975)

Matematiceskij sbornik

Аналог формулы логарифмического вычета для решений эллиптических систем первого порядка и весовые оценки решений d-задачи

Н.Н. Тарханов (1982)

Sibirskij matematiceskij zurnal

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«Vanishing theorem» pour un fibré vectoriel holomorphe positif de rang quelconque

$μ$ -constant monodromy groups and marked singularities

$ω$ –weighted holomorphic Besov spaces on the unit ball in $C^{n}$

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

Алгебра непрерывных на сфере аналитических функций с совершенным множеством особенностей, и полиномиальная аппроксимация на толстых компактах в $ℂ^{n}$

Аналитические свойства эйлеровых произведений для конгруэнц-подгрупп $S p_{2} (ℤ)$

Аналитическое представление CR-функций

Аналог формулы логарифмического вычета для решений эллиптических систем первого порядка и весовые оценки решений d-задачи

Аппроксимация аналитических функций и пространств Тейхмюллера.

Асимптотическая аппроксимация логарифмического потенциала.

Асимптотически голоморфные функции и их применения

Currently displaying 21 – 40 of 337