Function theory in several complex variables

By 西野利雄, Norman Levenberg, 山口博史. 2001

930 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6eb9013e65d239862e0375020efacca1dd6a5d68

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Citations in the corpus

Honeycomb Lattice Potentials and Dirac Points (2012, unknown): “By the Weierstrass Preparation Theorem [11], we may write P pλ, zq “ Hpλ, zq ¨ P̃ pλ, zq for pλ, zq in some polydisc Ũ ” t|λ| ă ε3, |z| ă ε4u, where P̃ is a Weierstrass polynomial (see (8.5) below) and H is a nonvanishing analytic function.”
Toeplitz operators and Carleson measures in strongly pseudoconvex domains (2012, background): “, [1, 2, 20, 23] for definitions, basic properties and applications to geometric function theory of the Kobayashi distance; and [19, 18, 24, 36] for definitions and basic properties of the Bergman kernel.”
The C-property for slice regular functions and applications to the Bergman space (2013, background): “1 of [18], implies that the convergence in the norm of A2(Ω) implies the uniformly convergence on compact subsets of Ω.”
Commuting Toeplitz operators on the polydisk (2003, unknown): “See Chapter 2 of [7] for details.”
The Bergman projection in $L^p$ for domains with minimal smoothness (2012, background): “As is well known, for each z ∈D, the function B(w,z) belongs to L(2)(D), see [K].”
The Schwarz lemma at the boundary (2010, methodology): “Then, by Harnack’s inequality [2], we have for 05r5R that”
An elliptic semilinear equation with source term involving boundary measures: the subcritical case (2000, background): “bounded open set. For the lower estimate of (2.8), see [ 21 ].”
Norm preserving extensions of holomorphic functions from subvarieties of the bidisk (2004, background): “Note that if V is a variety and f is holomorphic on V , then a baby theorem in the Cartan theory would be that there exists a neighborhood U ⊇ V and a holomorphic function g on U with f = g|V , though such a g might well not be unique.”
The Bergman kernel and projection on non-smooth worm domains (2007, methodology): “It is obvious from the transformation rule of the Bergman kernel (see [Kr1]) that it suffices to obtain the expression for the kernel in one of the two domains.”