ORCID Profile
0000-0002-1200-6595
Current Organisations
Western Australian Museum
,
Murdoch University
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Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 1999
Publisher: Springer Science and Business Media LLC
Date: 12-1985
DOI: 10.1007/BF01161650
Publisher: Springer Science and Business Media LLC
Date: 06-1998
DOI: 10.1007/BF01332821
Publisher: American Mathematical Society (AMS)
Date: 1976
DOI: 10.1090/S0002-9939-1976-0417654-2
Abstract: An analogue of a theorem of S. N. Bernstein is developed for certain metric locally compact abelian groups. This, together with a corresponding Jackson-type theorem, gives a characterisation in terms of their Fourier transforms of the Lipschitz functions defined on a compact abelian group with finite topological dimension.
Publisher: No publisher found
Publisher: Springer Science and Business Media LLC
Date: 09-1988
DOI: 10.1007/BF01184673
Publisher: Elsevier BV
Date: 03-2014
Publisher: Cambridge University Press (CUP)
Date: 10-1996
DOI: 10.1017/S1446788700000227
Abstract: In this paper we make use of semigroup methods on the space of compactly supported measures to obtain a Bochner representation for α-bounded positive-definite functions on a commutative hypergroup.
Publisher: Cambridge University Press (CUP)
Date: 04-2000
DOI: 10.1017/S1446788700001956
Abstract: In this paper we consider pseudo differential operators on local Hardy spaces h p (0 p ≤ 1) on Chébli-Trimèche hypergroups of exponential growth.
Publisher: Cambridge University Press (CUP)
Date: 04-1975
DOI: 10.1017/S000497270002390X
Abstract: Let G be a Hausdorff locally compact abelian group. The author has shown ( Bull. Austral. Math. Soc . 10 (1974), 59–66) that, given ε 0 and a certain base { V i } i ∈ I of symmetric open neighbourhoods of zero, the algebra L 1 ( G ) admits a bounded positive approximate unit { k i } i ∈ I such that for every p –th integrable function f on G , where ω( p f V i ) denotes the mean modulus of continuity with exponent p of f . The purpose of this paper is to obtain { k i } i ∈ I (as above) with a simple dependence of supp on { k i } i ∈ I on V i this is achieved for finite products and homomorphic images of groups for which such a simple dependence is known. The results obtained are used to give a simplified proof of the classical Jackson's Theorem for the circle group, and an analogue of this theorem for the a-adic solenoid.
Publisher: Mathematical Sciences Publishers
Date: 04-1982
Publisher: Cambridge University Press (CUP)
Date: 02-1986
DOI: 10.1017/S0004972700002914
Abstract: Every hermitian hypergroup structure on the set of nonnegative integers can be generated by a family of real-valued continuous functions defined on a compact interval. we characterise such structures in terms of properties of the generating functions.
Publisher: American Mathematical Society (AMS)
Date: 1980
DOI: 10.1090/S0002-9939-1980-0567988-7
Abstract: Let G denote a compact abelian group, and A p {A^p} the space of functions continuous on G and having p -summable Fourier transforms. The idempotent multipliers from A p {A^p} to A q {A^q} are characterised for p , q ∈ [ 1 , 2 ] p,q \\in [1,2] .
Publisher: Cambridge University Press (CUP)
Date: 02-1974
DOI: 10.1017/S1446788700015950
Abstract: This paper is concerned with version of Bernstein's inequality for Hausdroff locally compact Abelian groups. The ideas used are suggested by Exercise 12, p. 17 of Katznelson's book [4].
Publisher: Cambridge University Press (CUP)
Date: 08-1987
DOI: 10.1017/S0004972700026307
Abstract: In this note translation-invariant Dirichlet forms on a commutative hypergroup are studied. The main theorem gives a characterisation of an invariant Dirichlet form in terms of the negative definite function associated with it. As an illustration constructions of potentials arising from invariant Dirichlet forms are given. The ex les of one- and two-dimensional Jacobi hypergroups yield specifications of invariant Dirichlet forms, particularly in the case of Gelfand pairs of compact type.
Publisher: Cambridge University Press (CUP)
Date: 08-1988
DOI: 10.1017/S1446788700032250
Abstract: Various criteria, in terms of forward differences and related operations on coefficients, are shown to imply that certain series on bounded Vilenkin groups represent integrable functions. These results include analogues of known integrability theorems for trigonometric series. The method of proof is to pass from the given series to a derived series, and to deduce the integrability of the original series from smoothness properties of the latter.
Publisher: Cambridge University Press (CUP)
Date: 06-1992
DOI: 10.1017/S1446788700035102
Abstract: Let K 1 , K 2 be locally compact hypergroups. It is shown that every isometric isomorphism between their measure algebras restricts to an isometric isomorphism between their L 1 -algebras. This result is used to relate isometries of the measure algebras to homeomorphisms of the underlying locally compact spaces.
Publisher: Springer Science and Business Media LLC
Date: 07-1988
DOI: 10.1007/BF01246630
Publisher: Canadian Mathematical Society
Date: 10-1998
Abstract: In this paper we consider Fourier multipliers on local Hardy spaces h p (0 p ≤ 1) for Chébli-Trimèche hypergroups. The molecular characterization is investigated which allows us to prove a version of Hörmander’s multiplier theorem.
Publisher: Mathematical Sciences Publishers
Date: 09-1975
Publisher: Cambridge University Press (CUP)
Date: 08-2005
DOI: 10.1017/S1446788700009319
Abstract: In this paper we investigate when negative definite functions on commutative hypergroups satisfy the Schoenberg criterion.
Publisher: Cambridge University Press (CUP)
Date: 10-1973
DOI: 10.1017/S0004972700043185
Abstract: Let G be a Hausdorff locally compact abelian group, Γ its character group. We shall prove that, if S is a translation-invariant subspace of L p ( G ) ( p ∈ [1, ∞]), for each a ∈ G and , then is relatively compact (where Σ( f ) denotes the spectrum of f ). We also obtain a similar result when G is a Hausdorff compact (not necessarily abelian) group. These results can be considered as a converse of Bernstein's inequality for locally compact groups.
Publisher: Informa UK Limited
Date: 15-10-2011
Publisher: Wiley
Date: 1987
Publisher: Springer Science and Business Media LLC
Date: 05-1994
DOI: 10.1007/BF02572312
Publisher: Springer Science and Business Media LLC
Date: 04-2002
Publisher: Wiley
Date: 05-2000
Publisher: Springer Science and Business Media LLC
Date: 12-1981
DOI: 10.1007/BF01214758
Publisher: Cambridge University Press (CUP)
Date: 04-1981
DOI: 10.1017/S0004972700007073
Abstract: Let G denote a locally compact metrisable zero dimensional group with left translation invariant metric d . The Lipschitz spaces are defined by where a f : x → f ( ax ) and α 0 when r = ∞ the members of Lip(α r ) are taken to be continuous. For a suitable choice of metric it is shown that , where 1 ≤ p ≤ 2, α q −1 , p, q are conjugate indices and . It is also shown that for G infinite the range of values of α cannot be extended.
Publisher: World Scientific Pub Co Pte Lt
Date: 09-2000
DOI: 10.1142/S021902570000025X
Abstract: In this paper we study certain maximal functions for a class of Chébli–Trimèche hypergroups. Versions of the standard maximal theorems for these maximal functions are established and some applications are given.
Publisher: Elsevier BV
Date: 1981
Publisher: Cambridge University Press (CUP)
Date: 04-1985
DOI: 10.1017/S1446788700023119
Abstract: Let G be a locally compact abeian group, (μ ρ ) a net of bounded Radon measures on G . In this paper we consider conditions under which (μ ρ ) is saturated in L p ( G ) and apply these results to the Fejér and Picard approximation processes.
Publisher: Cambridge University Press (CUP)
Date: 12-1982
DOI: 10.1017/S1446788700018796
Abstract: In 1953 P. P. Korovkin proved that if ( T n ) is a sequence of positive linear operators defined on the space C of continuous real 2 π-periodic functions and lim T n f = f uniformly for f = 1, cos and sin, then lim T n f = f uniformly for all f ∈ C . Quantitative versions of this result have been given, where the rate of convergence is given in terms of that of the test functions 1, cos and sin, and the modulus of continuity of f . We extend this result by giving a quantitative version of Korovkin's theorem for compact connected abelian groups.
Publisher: Cambridge University Press (CUP)
Date: 02-1974
DOI: 10.1017/S0004972700040624
Abstract: If f is a p –th integrable function on the circle group and ω( p f δ) is its mean modulus of continuity with exponent p then an extended version of the classical theorem of Jackson states the for each positive integer n , there exists a trigonometric polynomial t n of degree at most n for which ‖f-t n ‖ p ≤(p f 1/n). In this paper it will be shewn that for G a Hausdorff locally compact abelian group, the algebra L 1 (G) admits a certain bounded positive approximate unit which, in turn, will be used to prove an analogue of the above result for L p (G).
Publisher: American Mathematical Society (AMS)
Date: 1975
DOI: 10.1090/S0002-9939-1975-0383000-5
Abstract: This paper is concerned with characterising, in terms of certain properties of their Fourier transforms, the Lipschitz functions of order α ( 0 α 1 ) \\alpha (0 \\alpha 1) defined on a locally compact metric 0 0 -dimensional Abelian group.
Publisher: Cambridge University Press (CUP)
Date: 12-1980
DOI: 10.1017/S1446788700016475
Abstract: In 1953 P. P. Korovkin proved that if ( T n ) is a sequence of positive linear operators defined on the space C of continuous real 2π-periodic functions and lim n →r T n f = f uniformly for f = 1, cos and sin. then lim n → r T n f = f uniformly for all f ∈ C . We extend this result to spaces of continuous functions defined on a locally compact abelian group G , with the test family {1, cos, sin} replaced by a set of generators of the character group of G .
No related grants have been discovered for Walter Russell Bloom.