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11.
In this paper we construct the conservation laws for the Camassa–Holm equation, the Dullin–Gottwald–Holm equation (DGH) and the generalized Dullin–Gottwald–Holm equation (generalized DGH). The variational derivative approach is used to derive the conservation laws. Only first order multipliers are considered. Two multipliers are obtained for the Camassa–Holm equation. For the DGH and generalized DGH equations the variational derivative approach yields two multipliers; thus two conserved vectors are obtained. 相似文献
12.
For 0<p<∞ and α>−1, we let denote the space of those functions f which are analytic in the unit disc and satisfy . In this paper we characterize the positive Borel measures μ in D such that , 0<p<q<∞. We also characterize the pointwise multipliers from to (0<p<q<∞) if p−2<α<p. In particular, we prove that if the only pointwise multiplier from to (0<p<q<∞) is the trivial one. This is not longer true for and we give a number of explicit examples of functions which are multipliers from to for this range of values. 相似文献
13.
We obtain characterizations of positive Borel measures μ on so that the nonisotropic potential space Kα[Lp(dσ)] is imbedded in the tent space T2q(dμ), where 1<p,q<+∞. We deduce characterizations for pointwise multipliers of the space Hαp. 相似文献
14.
The main objective of the paper is to characterize multipliers of summability fields of regular methods, while relaxing the usual boundedness condition. For this purpose we use the sequence spaces of A-bounded sequences and A-uniformly integrable sequences. Among the main results, it is shown that the space of multipliers is closely related to the space of A-statistically convergent sequences and that A-statistical convergence over ?∞ is equivalent to a regular matrix method. This observation eliminates the need for separate proofs of several A-statistical convergence results. 相似文献
15.
Jean-Paul Penot 《Mathematical Programming》1994,67(1-3):225-245
New second order optimality conditions for mathematical programming problems and for the minimization of composite functions are presented. They are derived from a general second order Fermat's rule for the minimization of a function over an arbitrary subset of a Banach space. The necessary conditions are more accurate than the recent results of Kawasaki (1988) and Cominetti (1989); but, more importantly, in the finite dimensional case they are twinned with sufficient conditions which differ by the replacement of an inequality by a strict inequality. We point out the equivalence of the mathematical programming problem with the problem of minimizing a composite function. Our conditions are especially important when one deals with functional constraints. When the cone defining the constraints is polyhedral we recover the classical conditions of Ben-Tal—Zowe (1982) and Cominetti (1990). 相似文献
16.
In this paper we are interested in conditions on the coefficients of a two-dimensional Walsh multiplier operator that imply the operator is bounded on certain of the Hardy type spaces Hp, 0<p<∞. We consider the classical coefficient conditions, the Marcinkiewicz-Hörmander-Mihlin conditions. They are known to be sufficient for the trigonometric system in the one and two-dimensional cases for the spaces Lp, 1<p<∞. This can be found in the original papers of Marcinkiewicz [J. Marcinkiewicz, Sur les multiplicateurs des series de Fourier, Studia Math. 8 (1939) 78-91], Hörmander [L. Hörmander, Estimates for translation invariant operators in Lp spaces, Acta Math. 104 (1960) 93-140], and Mihlin [S.G. Mihlin, On the multipliers of Fourier integrals, Dokl. Akad. Nauk SSSR 109 (1956) 701-703; S.G. Mihlin, Multidimensional Singular Integrals and Integral Equations, Pergamon Press, 1965]. In this paper we extend these results to the two-dimensional dyadic Hardy spaces. 相似文献
17.
Pascale Vitse 《Journal of Functional Analysis》2004,210(1):43-72
For Banach space operators T satisfying the Tadmor-Ritt condition ||(zI−T)−1||?C|z−1|−1, |z|>1, we prove that the best-possible constant CT(n) bounding the polynomial calculus for T, ||p(T)||?CT(n)||p||∞, deg(p)?n, behaves (in the worst case) as as n→∞. This result is based on a new free (Carleson type) interpolation theorem for polynomials of a given degree. 相似文献
18.
For Fourier expansions it will be shown that sharp
Marchaud-type inequalities follow from the positivity of the
Cesaro summability of some order. Some results of sharp
Marchaud-type will be derived using this method when other known
methods cannot be used. 相似文献
19.
K. T. Arasu Ka Hin Leung Siu Lun Ma Ali Nabavi D. K. Ray-Chaudhuri 《Designs, Codes and Cryptography》2006,41(1):111-123
A weighing matrix of weight k is a square matrix M with entries 0, ± 1 such that MM
T
= kI
n
. We study the case that M is a circulant and k = 22t
for some positive integer t. New structural results are obtained. Based on these results, we make a complete computer search for all circulant weighing
matrices of order 16.
相似文献
20.
In this article we are interested in conditions on the coefficients of a Walsh multiplier operator that imply the operator is bounded on certain dyadic Hardy spaces H p , 0 < p < ∞. In particular, we consider two classical coefficient conditions, originally introduced for the trigonometric case, the Marcinkiewicz and the Hörmander–Mihlin conditions. They are known to be sufficient in the spaces L p , 1 < p < ∞. Here we study the corresponding problem on dyadic Hardy spaces, and find the values of p for which these conditions are sufficient. Then, we consider the cases of H 1 and L 1 which are of special interest. Finally, based on a recent integrability condition for Walsh series, a new condition is provided that implies that the multiplier operator is bounded from L 1 to L 1, and from H 1 to H 1. We note that existing multiplier theorems for Hardy spaces give growth conditions on the dyadic blocks of the Walsh series of the kernel, but these growth are not computable directly in terms of the coefficients. 相似文献