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In mathematics in complex analysis, the concept of holomorphic separability is a measure of the richness of the set of holomorphic functions on a complex manifold or complex-analytic space.
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in complex analysis, the concept of holomorphicseparability is a measure of the richness of the set of holomorphic functions on a complex manifold or...
of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic so that, locally, they are power series in the variables...
varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of...
compact subset of X {\displaystyle X} . X {\displaystyle X} is holomorphicallyseparable, i.e. if x ≠ y {\displaystyle x\neq y} are two points in X {\displaystyle...
Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic functions. Geometric intuition plays an important role in many aspects...
compact space is continuous. If, in addition, fn are holomorphic, then the limit is also holomorphic. The uniform boundedness principle states that a pointwise...
{\displaystyle Y_{-n}(x)=(-1)^{n}Y_{n}(x).} Both Jα(x) and Yα(x) are holomorphic functions of x on the complex plane cut along the negative real axis...
Szabó for: Holomorphic disks and topological invariants for closed three-manifolds. Ann. of Math. (2) 159 (2004), no. 3, 1027–1158. Holomorphic disks and...
in general (under some slightly stronger hypotheses, on flatness and separability). Generically, then, such a morphism resembles a covering space in the...
f} is a fundamental one. Removable singularity – Undefined point on a holomorphic function which can be made regular Mathematical singularity – Point where...
holomorphic functions f in D that are continuous on the closure of D. As a result, the delta function δz is represented in this class of holomorphic functions...
algebra A ( D ) {\displaystyle A(\mathbf {D} )} consists of functions holomorphic in the open unit disk D ⊆ C {\displaystyle D\subseteq \mathbb {C} } and...
, P ( G ) {\displaystyle {\mathcal {P}}(G)} (of continuous, smooth, holomorphic, regular functions) on groups are Hopf algebras in the category (Ste...
separable if and only if its continuous dual is separable. This follows from the fact that for every normed space Y , {\displaystyle Y,} separability...
the ring H ( U ) {\displaystyle {\mathcal {H}}(U)} consisting of all holomorphic functions is an integral domain. The same is true for rings of analytic...
classical complex analysis, Montel's theorem asserts that the space of holomorphic functions on an open connected subset of the complex numbers has this...
Bourgain proved that the space H ∞ {\displaystyle H^{\infty }} of bounded holomorphic functions on the disk is a Grothendieck space. Dunford–Pettis property...
real coordinates x and y, where i represents the imaginary unit. Any holomorphic function w = f(z) with non-zero complex derivative will produce a conformal...
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