63,168 research outputs found
Correspondence between Samuel Ross Ballin, Ralph C. Talcott, Joseph S. Trovato, and Mary F. Walsh, 1969-1971
No full text4 leavesCorrespondence between Samuel Ross Ballin, Ralph C. Talcott, Joseph S. Trovato, and Mary F. Walsh, 1969-1971, regarding a paper Talcott was writing about Luks
Lacunary Fourier and Walsh-Fourier series near L1
No full textWe prove the following theorem: given a lacunary sequence of integers {nj}, the subsequences Fnj f and Wnj f of respectively the Fourier and the Walsh-Fourier series of f: T → C converge almost everywhere to (Formula presented.) Our integrability condition (1) is less stringent than the homologous assumption in the almost everywhere convergence theorems of Lie [14] (Fourier case) and Do and Lacey [6] (Walsh-Fourier case), where a triple-log term appears in place of the quadruple-log term of (1). Our proof of the Walsh-Fourier case is self-contained and, in antithesis to [6], avoids the use of Antonov's lemma [1, 19], relying instead on the novel weak-Lp bound for the lacunary Walsh-Carleson operator (Formula presented.). © 2013 Universitat de Barcelona
Electrodeposited lead dioxide coatings
No full textLead dioxide coatings on inert substrates such as titanium and carbon now offer new opportunities for a material known for 150 years. It is now recognised that electrodeposition allows the preparation of stable coatings with different phase structures and a wide range of surface morphologies. In addition, substantial modification to the physical properties and catalytic activities of the coatings are possible through doping and the fabrication of nanostructured deposits or composites. In addition to applications as a cheap anode material in electrochemical technology, lead dioxide coatings provide unique possibilities for probing the dependence of catalytic activity on layer composition and structure (critical review, 256 references)
ON (C, 1) SUMMABILITY OF INTEGRABLE FUNCTIONS WITH RESPECT TO THE WALSH-KACZMARZ SYSTEM
No full textLet G be the Walsh group. In this paper we prove for f ∈ L1(G) integrable functions the a.e. convergence σnf → f (n → ∞), where σn is the n-th (C, 1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator σ∗f: = supn |σnf |. We prove that σ ∗ is of type (p, p) for all 1 < p ≤ ∞ and of weak type (1, 1). Moreover, ‖σ∗f‖1 ≤ c‖|f |‖H, where H is the Hardy space on the Walsh group
Erratum to: Effect of moderate red wine intake on cardiac prognosis after recent acute myocardial infarction of subjects with Type 2 diabetes mellitus (Diabetic Medicine, (2006), 23, 9, (974-981), 10.1111/j.1464-5491.2006.01886.x)
No full textIn an article by Marfella et al, the author name C. Saron is incorrect and should be listed as C. Sardu. Therefore the correct author list is: R. Marfella, F. Cacciapuoti, M. Siniscalchi, F. C. Sasso, F. Marchese, F. Cinone, E. Musacchio, M. A. Marfella, L. Ruggiero, G. Chiorazzo, D. Liberti, G. Chiorazzo, G. F. Nicoletti, C. Sardu, F. D'Andrea, C. Ammendola, M. Verza and L. Coppola.In an article by Marfella et al, the author name C. Saron is incorrect and should be listed as C. Sardu. Therefore the correct author list is: R. Marfella, F. Cacciapuoti, M. Siniscalchi, F. C. Sasso, F. Marchese, F. Cinone, E. Musacchio, M. A. Marfella, L. Ruggiero, G. Chiorazzo, D. Liberti, G. Chiorazzo, G. F. Nicoletti, C. Sardu, F. D'Andrea, C. Ammendola, M. Verza and L. Coppola
Lestes inaequalis , Walsh
No full text27. L. Inaequalis, Walsh, l. c. (1862). Illinois.Published as part of Kirby, W. F., 1890, Genus Lestes, pp. 160-163 in A Synonymic Catalogue of Neuroptera Odonata, or Dragonflies. With an Appendix of fossil species, London :Gurney & Jackson on page 162, DOI: 10.5281/zenodo.352445
WALSH FOURIER 계수에 관한 연구
No full textUsing Marcinkiewicz interpolation theorem, Paley obtained some important theorems on Fourier coefficients. Later Hardy and Littlewood applied the theorems to trigonmetric Fourier coefficients and was able to give necessary and sufficient condition that a certain sequence of numbers should be the trigonmetric Fourier coefficients of a function in some L^(p).
In this thesis we show that the similar theorems hold for Walsh Fourier Coefficients, that is, as the main theorem, we show the following
(i) A necessary and sufficient condition that numbers c_(n)→0 should be, for every variation of their arrangement, the Walsh Fourier coefficients of a function fεL^(q), is that β*_(q,w)[c]&lt;∞. If the condition is satisfied, then ∥f∥_(q)≤A_(q)β*_(q,w)[c] for every such f.
(ii) A necessary aid sufficient condition that the c_(n) should be, for some variation of their arrangement, the Walsh Fourier coefficients of an fεL^(p), is that β_(p,w)*[c]&lt;∞. Moreover, we have β*_(p,w)[c]≤A_(p)∥f∥_(p) for every such f.;Paley 는 Marcinkiewicz Interpolation 정리를 사용하여 Fourier 계수에 관한 중요한 정리들을 얻었다. 그 후에 Hardy 와 Littlewood 가 그 정리들을 trigonometric Fourier 계수에 적용시키고 어떤 수열이 L^(p) 에 속하는 함수의 trigonometric Fourier 계수가 되는 필요충분조건을 주었다.
이 논문에서 우리는 Walsh Fourier 계수에 대해서도 비슷한 정리가 성립한다는 것, 즉, 아래와 같은 정리를 보인다 :
(1) 0으로 수렴하는 수열 c_(n) 이 그 수열의 배열의 변환에 관계없이 L^(q) 속하는 함수의 Walsh Fourier 계수가 되는 필요충분조건은 β_(q,w)^(*)[c]^( &lt; ∞) 이다.
만약 의의 조건이 만족되면 모든 함수 f 에 대해서 ∥f∥_(q□) A&apos;_(q)β^(*)_(q,w)[c] 가 성 립한다.
(2) 수열 c_(n) 이 그 수열의 배열의 어떤 변환에 대하여 L^(p) 에 속하는 함수의 Walsh Fourier 계수가 되는 필요충분조건은 β_(p)^(*)_(w)[c]^( &lt; ∞) 이다. 더 나아가서 우리는 그러한 모든 함수 f에 대해서 β_(q,w)^(*)[c] □ A_(p) ∥f∥_(p) 인 관계를 얻는다.ABSTRACT = ⅰ
CONTENTS = ⅱ
Ⅰ. INTRODUCTION = 1
Ⅱ. PRELIMINARIES = 2
A. MARCINKIEWICZ INTERPOLATION THEOREM = 2
B. PALEY&apos;S THEOREMS ON FOURIER COEFFICIENTS = 4
C. THEOREMS OF HARDY AND LITTLEWOOD ABOUT REARRANGEMENTS OF TRIGONOMETRIC FOURIER COEFFICIENTS = 9
D. PROPERTIES OF THE WALSH FUNCTIONS = 11
Ⅲ. WALSH VERSION OF PALEY&apos;S THEOREMS ON FOURIER COEFFICIENTS = 13
Ⅳ. WALSH VERSION OF HARDY AND LITTLEWOOD THEOREM ABOUT REARRANGEMENTS OF FOURIER COEFFICIENTS = 15
REFERENCES = 19
논문초록 = 2
Maximal estimates for the (C, alpha) means of d-dimensional Walsh-Fourier series
No full textThe d-dimensional dyadic martingale Hardy spaces H(p) are introduced and it is proved that the maximal operator of the (C, alpha) (alpha = (alpha(1),..., alpha(d))) means of a Walsh-Fourier series is bounded from H(p) to L(p) (1/(alpha(k) + 1) < p < infinity) and is of weak type(L(1), L(1)), provided that the supremum in the maximal operator is taken over a positive cone. As a consequence we obtain that the (C, alpha) means of a function f is an element of L(1) converge a.e. to the function in question. Moreover, we prove that the (C; alpha) means are uniformly bounded on H(p) whenever 1/(alpha(k) + 1)< p < infinity. Thus, in case f is an element of H(p), the (C; alpha) means converge to f in H(p) norm. The same results are proved for the conjugate (C; alpha) means, too
On the maximal operator of Walsh-Kaczmarz-Fejér means
No full textsummary:In this paper we prove that the maximal operator where is the -th Fejér mean of the Walsh-Kaczmarz-Fourier series, is bounded from the Hardy space to the space $L_{1/2}( G).
(C,α) summability of Walsh–Kaczmarz–Fourier series
No full textAbstractThe Walsh system will be investigated in the Kaczmarz rearrangement. In an earlier paper we have shown that the maximal operator of the (C,1)-means of the Walsh–Kaczmarz–Fourier series is bounded from the dyadic Hardy space Hp into Lp for every 12<p⩽1. In the present work, we extend this result to the (C,α) means when 0<α⩽1 and prove their maximal operator σα:Hp→Lp is bounded for all 1/(α+1)<p⩽1. By known results on interpolation we get from this theorem that σα is of weak type (1,1) and bounded from Lq into Lq if 1<q⩽∞. Moreover, the (C,α) means of an integrable function f converge to f a.e
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