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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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...
متن کاملOn rearrangements of vector-valued Hi-functions
Here fd(s)=fd(s+ 1), S<0. Davis' original proof uses probabilistic methods. Later J. L. Lewis (unpublished) gave an analytic proof. See also [6] for another proof, and also see [5], for related work. After the initial preparation of the paper, Professor Davis informed the author of the existence of another solution of the rearrangement problem due to O. D. Ceretelli [3], who shows that f has a ...
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This paper addresses the problem of evaluating a subset of the range of a vector-valued function. It is based on a work by Goldsztejn and Jaulin which provides methods based on interval analysis to address this problem when the dimension of the domain and co-domain of the function are equal. This paper extends this result to vector-valued functions with domain and co-domain of different dimensi...
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ژورنال
عنوان ژورنال: Zeitschrift für Analysis und ihre Anwendungen
سال: 2005
ISSN: 0232-2064
DOI: 10.4171/zaa/1261