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- W2225175488 abstract "Throughout this paper, all functions and vector spaces we shall consider are complex, m and n are fixed integers ≥1, E ≡ ℝn is the Euclidean n-space of all n-tuples of real numbers, P≡Pm-1 is the (complex) vector space of dimension $$(mathop nlimits^{m + n - 1} )$$(1)of all polynomials in n variables of (total) degree ≤m-1, |.| is the (Sobo-lev-like) seminorm (of kernel P) generated by the rotation invariant semi-inner product (on various suitable spaces of distributions to be specified later) where $$(v,w): = sumlimits_{{i_1},...,{i_m} = 1}^n {int_{{mathbb{R}^n}} {{partial _i}.{i_m}v( times ){partial _{{i_1}}}} ...{i_m}mathop wlimits^ - (x)dx}$$(2)where ({partial _{{i_1}}}...{i_m}: = {partial ^m}/partial {x_{{i_1}}}...partial {x_{{i_m}}}) is to be interpreted in the distributional sense. All integrals will be taken with respect to the Lebesgue measure on E (this is quite natural in view of the importance of translations of E). As usual, V denotes the vector space of test functions in E (i.e., infinitely differentiable functions with compact support in E), provided with the canonical Schwartz topology, while V (i.e., the dual of V) is the vector space of distributions in E." @default.
- W2225175488 created "2016-06-24" @default.
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- W2225175488 date "1979-01-01" @default.
- W2225175488 modified "2023-09-24" @default.
- W2225175488 title "A Convolution Approach to Multivariate Representation Formulas" @default.
- W2225175488 cites W1973000617 @default.
- W2225175488 doi "https://doi.org/10.1007/978-3-0348-6289-9_13" @default.
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