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Maps from the Two-Ball to the Three-Ball.

James J. Faran (1982)

Inventiones mathematicae

Matrices of positive polynomials.

Handelman, David (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Maximum module principle for power series on a Banach algebra.

Bezanilla L., Arnoldo, Contreras J., Roberto (2004)

Divulgaciones Matemáticas

Maximum modulus in a bidisc of analytic functions of bounded $𝐋$ -index and an analogue of Hayman’s theorem

Andriy Bandura, Nataliia Petrechko, Oleh Skaskiv (2018)

Mathematica Bohemica

We generalize some criteria of boundedness of $𝐋$ -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p + 1)$ th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).

Maximum modulus sets

Thomas Duchamp, Edgar Lee Stout (1981)

Annales de l'institut Fourier

We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain $D$ of dimension $N$ . If $Σ \subset b D$ is a smooth manifold of dimension $N$ and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in $A^{2} (D)$ with the same smooth $N$ -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in $H_{1} (D, R)$ vanishes or if $\overline{D} \subset C^{N}$ is polynomially...

Maximum modulus sets and reflection sets

Alexander Nagel, Jean-Pierre Rosay (1991)

Annales de l'institut Fourier

We study sets in the boundary of a domain in $C^{n}$ , on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to reflection sets, which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.

m-Berezin transform and compact operators.

Kyesook Nam, Dechao Zheng, Changyong Zhong (2006)

Revista Matemática Iberoamericana

m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L∞ is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary...

Mean growth and Fourier coefficients of some classes of holomorphic functions on bounded symmetric domains

Manfred Stoll (1985)

Annales Polonici Mathematici

Mean value theorems for harmonic and holomorphic functions on bounded symmetric domains.

M. Stoll (1977)

Journal für die reine und angewandte Mathematik

Meilleure approximation polynomiale et croissance des fonctions entières sur certaines variétés algébriques affines

Ahmed Zeriahi (1987)

Annales de l'institut Fourier

Soit $K$ un compact polynomialement convexe de $C^{n}$ et $V_{K}$ son “potentiel logarithmique extrémal” dans $C^{n}$ . Supposons que $K$ est régulier (i.e. $V_{K}$ continue) et soit $f$ une fonction holomorphe sur un voisinage de $K$ . On construit alors une suite ${P_{ℓ}}_{ℓ \geq 1}$ de polynôme de $n$ variables complexes avec deg $(P_{)} \leq ℓ$ pour $ℓ \geq 1$ , telle que l’erreur d’approximation $\max_{z \in K} | f (z) - P_{ℓ} (z) |$ soit contrôlée de façon assez précise en fonction du “pseudorayon de convergence” de $f$ par rapport à $K$ et du degré de convergence $ℓ$ . Ce résultat est ensuite utilisé pour étendre...