共查询到20条相似文献,搜索用时 15 毫秒
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M.M Rao 《Journal of Functional Analysis》1980,39(1):23-41
A characterization of local functionals on C∞(G), the space of real continuous functions with compact supports on a locally compact space G, is given. Such functionals were defined by Gel'fand and Vilenkin, as they occur in the analysis of generalized random processes with independent values. The preceding characterization is then used in a representation of the characteristic functionals of the above processes on C∞(G), and results analogous to those of Gel'fand and Vilenkin on a Schwartz space are obtained. Since C∞(G) is not nuclear, this study presents new problems and it largely complements the earlier work. 相似文献
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Let G be a metric locally compact Abelian group. We prove that the spaces (L1, Lip(α, p)), (L1, lip(α, p)), Lip(α, p) and lip(α, p)~ are isometrically isomorphic, where Lip(α, p) and lip(α, p) denote the Lipschitz spaces defined on G, (L1, A) is the space of multipliers from L1 to A, and lip(α, p)~ denotes the relative completion of lip(α, p). We also show that . 相似文献
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Joseph Max Rosenblatt 《Journal of Functional Analysis》1976,21(1):31-51
For a nondiscrete σ-compact locally compact Hausdorff group G, L∞(G) is a commutative Banach algebra under pointwise multiplication which has many nonzero proper closed invariant ideals; there is at least a continuum of maximal invariant ideals {Nα} such that Nα1 + Nα2 = L∞(G) whenever α1 ≠ α2. It follows from the construction of these ideals that when G is also amenable as a discrete group, then LIM?TLIM contains at least a continuum of mutually singular elements each of which is singular to any element of TLIM. The supports of left-invariant means are in the maximal ideal space of L∞(G); the structure of these supports leads to the notion of stationary and transitive maximal ideals. To prove that both these types of maximal ideals are dense among all maximal ideals, one shows that the intersection of all nonzero closed invariant ideals is zero. This is the case even though the intersection of any sequence of closed invariant ideals is not zero and the intersection of all the maximal invariant ideals is not zero. 相似文献
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Let G be a locally compact abelian group. A translation-invariant subspace in L1(G) may or may not be complemented depending on the structure of its hull in ?. Techniques for deciding this complementation problem in a variety of situations are developed and illustrated with examples. A complete characterization is obtained for those ideals with a discrete hull. 相似文献
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J. Extremera 《Journal of Functional Analysis》2003,197(1):212-227
Let G be a compact group. If the trivial representation of G is not weakly contained in the left regular representation of G on L02(G) and X is either Lp(G) for 1<p?∞ or C(G), then we show that every complete norm |·| on X that makes translations from (X,|·|) into itself continuous is equivalent to ||·||p or ||·||∞ respectively. If 1<p?∞ and every left invariant linear functional on Lp(G) is a constant multiple of the Haar integral, then we show that every complete norm |·| on Lp(G) that makes translations from (Lp(G),|·|) into itself continuous and that makes the map t?Lt from G into bounded is equivalent to ||·||p. 相似文献
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Stephen T.L Choy 《Journal of Mathematical Analysis and Applications》1983,97(2):337-346
The problem of defining a convolution of operator-valued measures defined on a locally compact semitopological semigroup which represent weakly compact operators is considered in this paper. Convolution of the corresponding weakly compact operators is then defined. A characterization of multipliers on function spaces is given in terms of their representing measures. 相似文献
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Various initial-boundary value problems and Cauchy problems can be written in the form , where ?:R→ is nondecreasing and A is the linear generator of strongly continuous nonexpansive semigroup e?tA in an L1 space. For example, if A = ?Δ (subject, perhaps, to suitable boundary conditions) we obtain equations arising in flow in a porous medium or plasma physics (depending on the choice of ?) while if acting in L1() we have a scalar conservation law. In this paper we show that if M, m > 0 and m?′2 ? ν??′' ? M?′2, where ν ? {1,?1}, then (roughly speaking), the norm of may be estimated in terms of the initial data u0 in L1. Such estimates give information about the regularity of solutions, asymptotic behaviour, etc., in applications. Side issues, such as the introduction of sufficiently regular approximate problems on which estimates can be made and the assignment of a precise meaning to the operator A?, are also dealt with. These considerations are of independent interest. 相似文献
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Amédée Debiard 《Journal of Functional Analysis》1981,40(2):185-265
Growth of harmonic functions and boundary values in a Sobolev space; comparison between the Hp space associated to Calderón Lusin's area integral and the Hp space associated to the maximal admissible function; study of Littlewood-Paley functions for the harmonic functions for the invariant laplacian of the hermitian hyperbolic space; relation between a Littlewood-Paley function and the bounded mean oscillation functions; study of H1 and H1 B.M.O. duality. 相似文献
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A theory for strongly singular integrals on spaces of homogeneous type is developed and used to obtain sharp multiplier theorems for various groups. 相似文献
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D.F Holt 《Journal of Algebra》1979,60(2):307-318
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Wolfgang Lusky 《Journal of Functional Analysis》1985,62(1):1-7
It is shown that every separable Banach space X containing a subspace isomorphic to c0 has a subspace Y with basis such that and the latter space has a shrinking basis and an unconditional FDD. Moreover, it is shown that X ⊕ C∞ has a basis if X has the bounded approximation property. 相似文献
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We study positive C0-semigroups on Lp associated with second-order uniformly elliptic divergence-type operators with singular lower-order terms, subject to a wide class of boundary conditions. We obtain an interval (pmin, pmax) in the Lp-scale where these semigroups can be defined, including the case 2∉(pmin, pmax). We present an example showing that the result is optimal. We also show that the semigroups are analytic with angles of analyticity and spectra of the generators independent of p, for the whole range of p where the semigroups are defined. 相似文献
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The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc. 相似文献
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Zeev SobolHendrik Vogt 《Journal of Functional Analysis》2002,193(1):24-54
We study Lp-theory of second-order elliptic divergence-type operators with measurable coefficients. To this end, we introduce a new method of constructing positive C0-semigroups on Lp associated with sesquilinear (not necessarily sectorial) forms in L2. A precise condition ensuring that the elliptic operator is associated with a quasi-contractive C0-semigroup on Lp is established. 相似文献
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In this paper, the problem of when the sub-direct sum of two strictly diagonally dominant P-matrices is a strictly diagonally dominant P-matrix is studied. In particular, it is shown that the subdirect sum of overlapping principal submatrices of strictly diagonally dominant P-matrices is a strictly diagonally dominant P-matrix. It is also established that the 2-subdirect sum of two totally nonnegative matrices is a totally nonnegative matrix under some conditions. It is obtained that a partial totally nonnegative matrix, whose graph of the specified entries is a monotonically labeled 2-chordal graph, has a totally nonnegative completion. Finally, a positive answer to the question (IV) in Fallat and Johnson [Shaun M. Fallat, C.R. Johnson, J.R. Torregrosa, A.M. Urbano, P-matrix completions under weak symmetry assumptions, Linear Algebra Appl. 312 (2000) 73-91] is given for P0-matrices. 相似文献
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