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Displaying 681 – 700 of 1395

Non-homogeneous directional equations: Slice solutions belonging to functions of bounded $L$ -index in the unit ball

Andriy Bandura, Tetyana Salo, Oleh Skaskiv (2024)

Mathematica Bohemica

For a given direction $𝐛 \in ℂ^{n} ∖ {0}$ we study non-homogeneous directional linear higher-order equations whose all coefficients belong to a class of joint continuous functions which are holomorphic on intersection of all directional slices with a unit ball. Conditions are established providing boundedness of $L$ -index in the direction with a positive continuous function $L$ satisfying some behavior conditions in the unit ball. The provided conditions concern every solution belonging to the same class of functions...

Non-solvability of the tangential ${\bar{\partial}}_{M}$ -systems

Giuseppe Zampieri (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove that for a real analytic generic submanifold $M$ of $C^{n}$ whose Levi-form has constant rank, the tangential ${\bar{\partial}}_{M}$ -system is non-solvable in degrees equal to the numbers of positive and $M$ negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with $M$ non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.

Non-Vanishing of the Bergman Kernel Function at Boundary Points of Certain Domains in Cn .

Steven R. Bell (1979)

Mathematische Annalen

Norm and Taylor coefficients estimates of holomorphic functions in balls

Jacob Burbeam, Do Young Kwak (1991)

Annales Polonici Mathematici

A classical result of Hardy and Littlewood states that if $f (z) = \sum_{m = 0}^{\infty} a_{m} z^{m}$ is in $H^{p}$ , 0 < p ≤ 2, of the unit disk of ℂ, then $\sum_{m = 0}^{\infty} {(m + 1)}^{p - 2} {| a_{m} |}^{p} \leq c_{p} ∥ f ∥_{p}^{p}$ where $c_{p}$ is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of $ℂ^{n}$ , and use this extension to study some related multiplier problems in $ℂ^{n}$ .

Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball.

Clahane, Dana D., Stević, Stevo (2006)

Journal of Inequalities and Applications [electronic only]

Normal families of bicomplex meromorphic functions

Kuldeep Singh Charak, Dominic Rochon, Narinder Sharma (2012)

Annales Polonici Mathematici

We introduce the extended bicomplex plane 𝕋̅, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about convergence of sequences of bicomplex meromorphic functions. Hence the concept of normality of a family of bicomplex meromorphic functions on bicomplex domains emerges. Besides obtaining a normality criterion for such families, the bicomplex analog of the Montel theorem for meromorphic functions and the fundamental normality tests for families...

Normal families of holomorphic functions on infinite-dimensional spaces.

Takatsuka, Paula (2006)

Portugaliae Mathematica. Nova Série

Normal families of meromorphic mappings of several complex variables into ℂPⁿ for moving hypersurfaces

Si Duc Quang, Tran Van Tan (2008)

Annales Polonici Mathematici

We prove some normality criteria for families of meromorphic mappings of a domain $D \subset ℂ^{m}$ into ℂPⁿ under a condition on the inverse images of moving hypersurfaces.

Normal families of proper holomorphic correspondences.

W. Klingenberg, S. Pinchuk (1991)

Mathematische Zeitschrift

Normed domains of holomorphy.

Krantz, Steven G. (2010)

International Journal of Mathematics and Mathematical Sciences

Note on convergence and orders of vanishing along curves.

Shuzo Izumi (1990)

Manuscripta mathematica

Note on integral representation of holomorphic functions in several complex variables

Chen Shu-Jin (1989)

Rendiconti del Seminario Matematico della Università di Padova

Noyau de Bergman et applications biholomorphes dans des domaines strictement pseudo-convexes

Nessim Sibony (1974/1975)

Séminaire Bourbaki

Nullstellensatz and cycles of zeroes of holomorphic mappings

Ewa Cygan (2002)

Annales Polonici Mathematici

The local Nullstellensatz exponent for holomorphic mappings via intersection theory for the cases of isolated and quasi-complete intersection is considered.

On 3-graded Lie algebras, Jordan pairs and the canonical kernel function.

De Oliveira, M.P. (2003)

Electronic Research Announcements of the American Mathematical Society [electronic only]

On a boundary version of Morera's theorem.

Myslivets, S.G. (2001)

Sibirskij Matematicheskij Zhurnal

On a characterization of the analytic and meromorphic functions defined on some rigid domains

Capi Corrales Rodrigáñez (1994)

Journal de théorie des nombres de Bordeaux

On a class of tangential Cauchy-Riemann maps

Alois Švec (1977)

Commentationes Mathematicae Universitatis Carolinae

On a class of $\bar{\partial}$ -equations without solutions

Telemachos Hatziafratis (1998)

Commentationes Mathematicae Universitatis Carolinae

In this note we construct $\bar{\partial}$ -equations (inhomogeneous Cauchy-Riemann equations) without solutions. The construction involves Bochner-Martinelli type kernels and differentiation with respect to certain parameters in appropriate directions.

On a Domain Equivalent to the Bidisk.

John Wermer (1980)

Mathematische Annalen

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