摘要 :
We study the classification of holomorphic isometric embeddings of the unit disk into polydisks. As a corollary of our results, we can give a complete classification when the target is the 2-disk and the 3-disk. We also prove that...
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We study the classification of holomorphic isometric embeddings of the unit disk into polydisks. As a corollary of our results, we can give a complete classification when the target is the 2-disk and the 3-disk. We also prove that the holomorphic isometric embeddings between polydisks are induced by those of the unit disk into polydisks.
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Let P_1 be a polydisk and P_2 =Φ(P_1) where φ is a certain symplectic fold. We determine sharp lower bounds on the size of a ball containing the support of a symplectomorphism mapping P_1 to P_2. Optimal symplectomorphisms are t...
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Let P_1 be a polydisk and P_2 =Φ(P_1) where φ is a certain symplectic fold. We determine sharp lower bounds on the size of a ball containing the support of a symplectomorphism mapping P_1 to P_2. Optimal symplectomorphisms are the folds themselves. As a result, we construct symplectically nonisotopic polydisks in balls and in the complex projective plane.
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For the corona problem on the bidisk, we find analytic solutions belonging to the Orlicz-type space $\exp {\left( {L^{{\frac{1}{3}}} } \right)}.$ In addition, for 1 ≤ p < ∞, an $ \mathcal{H}^{p} {\left( {D^{2} } \right)}$ corona theorem is established. Similar techniques can be used for the polydisk....
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For the corona problem on the bidisk, we find analytic solutions belonging to the Orlicz-type space $\exp {\left( {L^{{\frac{1}{3}}} } \right)}.$ In addition, for 1 ≤ p < ∞, an $ \mathcal{H}^{p} {\left( {D^{2} } \right)}$ corona theorem is established. Similar techniques can be used for the polydisk.
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We introduce and study holomorphically finitely generated (HFG) Frechet algebras, which are analytic counterparts of affine (i.e., finitely generated) C-algebras. Using a theorem of O. Forster, we prove that the category of commut...
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We introduce and study holomorphically finitely generated (HFG) Frechet algebras, which are analytic counterparts of affine (i.e., finitely generated) C-algebras. Using a theorem of O. Forster, we prove that the category of commutative HFG algebras is anti-equivalent to the category of Stein spaces of finite embedding dimension. We also show that the class of HFG algebras is stable under some natural constructions. This enables us to give a series of concrete examples of HFG algebras, including Arens-Michael envelopes of affine algebras (such as the algebras of holomorphic functions on the quantum affine space and on the quantum torus), the algebras of holomorphic functions on the free polydisk, on the quantum polydisk, and on the quantum polyannulus.
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We study the continuity of composition operators on the classical Hardy and weighted Bergman spaces of the polydisk. We show that this problem involves some delicate properties of the derivative of the symbol. In particular, we ch...
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We study the continuity of composition operators on the classical Hardy and weighted Bergman spaces of the polydisk. We show that this problem involves some delicate properties of the derivative of the symbol. In particular, we characterize continuity when the symbol is a linear self-map of the polydisk.
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We study hyperbolic Gaussian analytic functions in the unit polydisk of C-n. Following the scheme previously used in the unit ball, we first study the asymptotics of fluctuations of linear statistics as the directional intensities...
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We study hyperbolic Gaussian analytic functions in the unit polydisk of C-n. Following the scheme previously used in the unit ball, we first study the asymptotics of fluctuations of linear statistics as the directional intensities L-j, j = 1, ..., n tend to infinity. Then, we estimate the probability of large deviations of such linear statistics and use the estimate to prove a hole theorem. Our proofs are inspired by the methods of M. Sodin and B. Tsirelson for the one-dimensional case, and B. Shiffman and S. Zelditch for the study of the analogous problem for compact Kahler manifolds.
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This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. Let U~n be the unit polydisk in C~nand S be the space of functions of regular variation. Let 1 ≤ p ≤ ∞, ω = (ω_1, ... ω_n),∈ S(...
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This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. Let U~n be the unit polydisk in C~nand S be the space of functions of regular variation. Let 1 ≤ p ≤ ∞, ω = (ω_1, ... ω_n),∈ S(1 ≤ j ≤ n) and f ∈ H (U~n). The function f is said to be an element of the holomorphic Besov space B_p(ω) .
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摘要 :
This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. Let U(n) be the unit polydisk in C(n) and S be the space of functions of regular variation. Let 1 展开
This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. Let U(n) be the unit polydisk in C(n) and S be the space of functions of regular variation. Let 1 收起
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This paper studies products of Toeplitz operators on the Hardy space of the polydisk. We show that T_fT_g = 0 if and only if T_fT_g is a finite rank if and only if T_f or T_g is zero. The product T_fT_g is still a Toeplitz operato...
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This paper studies products of Toeplitz operators on the Hardy space of the polydisk. We show that T_fT_g = 0 if and only if T_fT_g is a finite rank if and only if T_f or T_g is zero. The product T_fT_g is still a Toeplitz operator if and only if there is a h ∈ L~∞(T~n) such that T_fT_g - T_h is a finite rank operator. We also show that there are no compact simi-commutators with symbols pluriharmonic on the polydisk.
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We study properties of composition operators induced by symbols acting from the unit disk to the polydisk. This result will be involved in the investigation of weighted composition operators on the Hardy space on the unit disk and...
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We study properties of composition operators induced by symbols acting from the unit disk to the polydisk. This result will be involved in the investigation of weighted composition operators on the Hardy space on the unit disk and, moreover, be concerned with composition operators acting from the Bergman space to the Hardy space on the unit disk.
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