共查询到20条相似文献,搜索用时 31 毫秒
1.
K. G. Ivanov 《Constructive Approximation》1986,2(1):377-392
The class of all continuous functions possessing n?α(1/p<α≤1) order of approximation by Bernstein polynomials inL p[0, 1] is characterized. 相似文献
2.
Angelo Favini Gisle Ruiz Goldstein Jerome A. Goldstein Silvia Romanelli 《Mathematische Nachrichten》2002,238(1):78-102
We deal with the problem of analyticity for the semigroup generated by the second order differential operator Au ≔ αu″ + βu′ (or by some restrictions of it) in the spaces Lp(0, 1), with or without weight, and in W1,p(0, 1), 1 < p < ∞. Here α and β are assumed real‐valued and continuous in [0, 1], with α(x) > 0 in (0, 1), and the domain of A is determined by the generalized Neumann boundary conditions and by Wentzell boundary conditions. 相似文献
3.
Michael I Ganzburg 《Journal of Approximation Theory》1998,92(3):379-410
We determine the exact order of best approximation by polynomials and entire functions of exponential type of functions like?λ, α(x)=|x|λ exp(−A|x|−α). In particular, it is shown thatE(?λ, α, n, Lp(−1, 1))∼n−(2λp+αp+2)/2p(1+α)×exp(−(1+α−1)(Aα)1/(1+α) cos απ/2(1+α) nα/(1+α)), whereE(?λ, α, n, Lp(−1, 1)) denotes best polynomial approximation of?λ, αinLp(−1, 1),λ∈,α∈(0, 2],A>0, 1?p?∞. The problem, concerning the exact order of decrease ofE(?0, 2, n, L∞(−1, 1)), has been posed by S. N. Bernstein. 相似文献
4.
A. A. Minzoni 《Studies in Applied Mathematics》1986,75(3):265-269
It is shown how a conjecture of G. B. Whitham on the completeness of the functions { ψ n } = { e?np(x) cos nx, e?np(x) sin nx } in the interval [0, 2π] is indeed true provided p has a Hölder continuous first derivative, i.e., p ∈ C1, α[0, 2π]. Also an elementary proof of Whitham's conjecture is given for p ∈ C2, α[0, 2π]. 相似文献
5.
We establish the formulas of the left‐ and right‐hand Gâteaux derivatives in the Lorentz spaces Γp,w = {f: ∫0α (f **)p w < ∞}, where 1 ≤ p < ∞, w is a nonnegative locally integrable weight function and f ** is a maximal function of the decreasing rearrangement f * of a measurable function f on (0, α), 0 < α ≤ ∞. We also find a general form of any supporting functional for each function from Γp,w , and the necessary and sufficient conditions for which a spherical element of Γp,w is a smooth point of the unit ball in Γp,w . We show that strict convexity of the Lorentz spaces Γp,w is equivalent to 1 < p < ∞ and to the condition ∫0∞ w = ∞. Finally we apply the obtained characterizations to studies the best approximation elements for each function f ∈ Γp,w from any convex set K ? Γp,w (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
Detlef Hühnlein Michael J. Jr. Jacobson Damian Weber 《Designs, Codes and Cryptography》2003,30(3):281-299
We present a new non-interactive public-key distribution system based on the class group of a non-maximal imaginary quadratic order Cl(
p
). The main advantage of our system over earlier proposals based on (Z/nZ)* [25,27] is that embedding id information into group elements in a cyclic subgroup of the class group is easy (straight-forward embedding into prime ideals suffices) and secure, since the entire class group is cyclic with very high probability. Computational results demonstrate that a key generation center (KGC) with modest computational resources can set up a key distribution system using reasonably secure public system parameters. In order to compute discrete logarithms in the class group, the KGC needs to know the prime factorization of
p
=1
p
2. We present an algorithm for computing discrete logarithms in Cl(
p
) by reducing the problem to computing discrete logarithms in Cl(1) and either F*
p
or F*
p
2. Our algorithm is a specific case of the more general algorithm used in the setting of ray class groups [5]. We prove—for arbitrary non-maximal orders—that this reduction to discrete logarithms in the maximal order and a small number of finite fields has polynomial complexity if the factorization of the conductor is known. 相似文献
7.
We consider twisted convolution operators with kernels having singularities on a sphere and having as Fourier transform the oscillatory symbol mα(|ξ|) = |ξ|–αei|ξ|, 0 ≤ ??α < 2n. We give integral representations for such operators and, as a principal result, we study Lp–Lq estimates for them. 相似文献
8.
San Ling 《Israel Journal of Mathematics》1993,84(3):365-384
Whenp, q are distinct odd primes, and γ:J
0(p)2×J
0(q)2→J
0(pq) is the natural map defined by the degeneracy maps, Ribet [10] determined the odd part of the kernel of γ. We study the 2-primary
part of this kernel through its intersection with the Eisenstein kernelJ
0(p)[I
p
)2×J
0(q)[I
q
]2. We determine this intersection forp≢1 mod 16,q≢1 mod 16, and also produce new elements of ker γ wheneverp≡9 mod 16 orq≡9 mod 16. These sharpen Ribet's results in [10]. 相似文献
9.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(11):1227-1230
We consider a semigroup of Markovian and symmetric operators to which we associate fractional Sobolev spaces Dαp (0 < α < 1 and 1 < p < ∞) defined as domains of fractional powers (−Ap)α/2, where Ap is the generator of the semigroup in Lp. We show under rather general assumptions that Lipschitz continuous functions operate by composition on Dαp if p ≥ 2. This holds in particular in the case of the Ornstein-Uhlenbeck semigroup on an abstract Wiener space. 相似文献
10.
Lars Diening 《Mathematische Nachrichten》2004,268(1):31-43
We study the Riesz potentials Iαf on the generalized Lebesgue spaces Lp(·)(?d), where 0 < α < d and Iαf(x) ? ∫equation/tex2gif-inf-3.gif |f(y)| |x – y|α – d dy. Under the assumptions that p locally satisfies |p(x) – p(x)| ≤ C/(– ln |x – y|) and is constant outside some large ball, we prove that Iα : Lp(·)(?d) → Lp?(·)(?d), where . If p is given only on a bounded domain Ω with Lipschitz boundary we show how to extend p to on ?d such that there exists a bounded linear extension operator ? : W1,p(·)(Ω) ? (?d), while the bounds and the continuity condition of p are preserved. As an application of Riesz potentials we prove the optimal Sobolev embeddings Wk,p(·)(?d) ?Lp*(·)(Rd) with and W1,p(·)(Ω) ? Lp*(·)(Ω) for k = 1. We show compactness of the embeddings W1,p(·)(Ω) ? Lq(·)(Ω), whenever q(x) ≤ p*(x) – ε for some ε > 0. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
San Ling 《Israel Journal of Mathematics》1997,99(1):29-54
Forp≥3 a prime, we compute theQ-rational cuspidal subgroupC(p
r
) of the JacobianJ
0(p
r
) of the modular curveX
0(p
r
). This result is then applied to determine the component group Φ
p
r
of the Néron model ofJ
0(p
r
) overZ
p
. This extends results of Lorenzini [7]. We also study the action of the Atkin-Lehner involution on thep-primary part ofC(p
r
), as well as the effect of degeneracy maps on the component groups. 相似文献
12.
Michael J. Johnson 《Constructive Approximation》2004,20(2):303-324
We show that the Lp-approximation order of surface spline interpolation
equals m+1/p for p in the range 1 \leq p \leq 2, where m is an integer
parameter which specifies the surface spline. Previously it was known that this
order was bounded below by m + &frac; and above by m+1/p. With
h denoting the fill-distance between the interpolation points and the domain
, we show specifically that the Lp()-norm of the error between f
and its surface spline interpolant is O(hm + 1/p) provided that f belongs
to an appropriate Sobolev or Besov space and that \subset
Rd is open, bounded, and has the C2m-regularity
property. We also show that the boundary effects (which cause the rate of
convergence to be significantly worse than O(h2m)) are confined to a
boundary layer whose width is no larger than a constant multiple of
h |log h|. Finally, we state numerical evidence which supports the
conjecture that the
Lp-approximation order of surface spline interpolation is m + 1/p for
2 < p \leq \infty. 相似文献
13.
Hironobu Sasaki 《偏微分方程通讯》2015,40(11):1959-2004
We study scattering problems for the one-dimensional nonlinear Dirac equation (?t + α?x + iβ)Φ = λ|Φ|p?1Φ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operators D(t)xD(?t) and t?x + x?t ? α/2, where {D(t)}t∈? is the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties of D(t)xD(?t) and t?x + x?t ? α/2. 相似文献
14.
V. R. Fatalov 《Theoretical and Mathematical Physics》2011,168(2):1112-1149
We obtain new asymptotic formulas for two classes of Laplace-type functional integrals with the Bogoliubov measure. The principal
functionals are the Lp functionals with 0 < p < ∞ and two functionals of the exact-upper-bound type. In particular, we prove theorems on the Laplace-type asymptotic
behavior for the moments of the Lp norm of the Bogoliubov Gaussian process when the moment order becomes infinitely large. We establish the existence of the
threshold value p
0
= 2+4π
2
/β
2
ω
2
, where β > 0 is the inverse temperature and ω > 0 is the harmonic oscillator eigenfrequency. We prove that the asymptotic behavior under investigation differs for 0 < p < p
0
and p > p
0
. We obtain similar asymptotic results for large deviations for the Bogoliubov measure. We establish the scaling property
of the Bogoliubov process, which allows reducing the number of independent parameters. 相似文献
15.
《Quaestiones Mathematicae》2013,36(4):505-514
AbstractIn this paper the concepts of ?mv-statistical convergence of order α and strong (p, ?m)-Ces`aro summability of order α are introduced for sequences of complex (or real) numbers. Some relations between the ?mv-statistical convergence of order α and strong (p, ?mv)-Ces`aro summability of order α are given. Also some relations between the space ωαp (?mv, f) and Sα (?mv) are examined. 相似文献
16.
New oscillation and nonoscillation theorems are obtained for the second order linear differential equationu″ + p(t)u = 0, wherep(t) ∈ C[0, ∞) andp(t) ≥ 0. Conditions only about the integrals ofp(t) on every interval [2nt0, 2n + 1t0] (n = 1, 2,…) for some fixedt0 > 0 are used in the results. 相似文献
17.
Filippo Gazzola Hans-Christoph Grunau 《Calculus of Variations and Partial Differential Equations》2007,30(3):389-415
We are interested in stability/instability of the zero steady state of the superlinear parabolic equation u
t
+ Δ2
u = |u|
p-1
u in , where the exponent is considered in the “super-Fujita” range p > 1 + 4/n. We determine the corresponding limiting growth at infinity for the initial data giving rise to global bounded solutions.
In the supercritical case p > (n + 4)/(n−4) this is related to the asymptotic behaviour of positive steady states, which the authors have recently studied. Moreover,
it is shown that the solutions found for the parabolic problem decay to 0 at rate t
−1/(p-1). 相似文献
18.
Let C(α) denote the finite interval graphs representable as intersection graphs of closed real intervals with lengths in [1, α]. The points of increase for C are the rational α ≥ 1. The set D(α) = [∩β>αC(β)]\C(α) of graphs that appear as soon as we go past α is characterized up to isomorphism on the basis of finite sets E(α) of irreducible graphs for each rational α. With α = p/q and p and q relatively prime, ∣E(α)∣ is computed for all (p,q) with q ? 2 and p = q + 1. When q = 1, E(p) contains only the bipartite star K1, p+2. A lowr bound on ∣E(α)∣ is given for all rational α. 相似文献
19.
We give elementary proofs of the fact that the Loewner matrices
[\fracf(pi) - f (pj)pi-pj]{[\frac{f(p_i) - f (p_j)}{p_i-p_j}]} corresponding to the function f(t) = t
r
on (0, ∞) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0, ∞) the Loewner matrices corresponding
to an operator convex function on (−1, 1) need not be conditionally negative definite. 相似文献