Vector-valued holomorphic and harmonic functions
نویسندگان
چکیده
منابع مشابه
Holomorphic vector-valued functions
exists. The function f is continuously differentiable when it is differentiable and f ′ is continuous. A k-times continuously differentiable function is C, and a continuous function is C. A V -valued function f is weakly C when for every λ ∈ V ∗ the scalar-valued function λ◦ f is C. This sense of weak differentiability of a function f does not refer to distributional derivatives, but to differe...
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If Q is a Widom domain in the plane (e.g., finitely connected) and / is any bounded harmonic function on Q which is not holomorphic, then we prove the algebra H°°(Sl)[f] contains all the uniformly continuous functions on ÎÎ . The basic tools are the solution of the 5 equation with L°° estimates and some estimates on the level sets of functions in BMOA.
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This important result is listed in the theorem on the next page. Note that the derivative of the vector-valued function is itself a vector-valued function. You can see from Figure 12.8 that is a vector tangent to the curve given by and pointing in the direction of increasing values. tr t r t r f t i g t j lim t→0 f t t f t t i lim t→0 g t t g t t j lim t→0 f t t f t t i g t t g t t j lim t→0 f ...
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In this letter, we provide a study of learning in a Hilbert space of vectorvalued functions. We motivate the need for extending learning theory of scalar-valued functions by practical considerations and establish some basic results for learning vector-valued functions that should prove useful in applications. Specifically, we allow an output space Y to be a Hilbert space, and we consider a repr...
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ژورنال
عنوان ژورنال: Concrete Operators
سال: 2016
ISSN: 2299-3282
DOI: 10.1515/conop-2016-0007