The Fourier transform of vector-valued functions
نویسندگان
چکیده
منابع مشابه
On the Vector Valued Fourier Transform and Compatibility of Operators*
is the dual group of G, and p ′ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform F G if F G ⊗ T : Lp(G)⊗X → Lp′ (G ′ )⊗ Y admits a continuous extension [F , T ] : [Lp(G), X ] → [Lp′ (G ′ ), Y ]. We show that if G is topologically isomorphic with R×Z×F, where l and m are nonnegative integers and F is a compact group with...
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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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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1985
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500005978