共查询到20条相似文献,搜索用时 343 毫秒
1.
The spectrum of each symmetric ψ DO of the symbol class S0
1, γ, 0≤γ<1, acting on B3
p,q(w(x)) and F3
p,q(w(x)), is independent of the choice ofs ∈ℝ, 0<p≤∞ (p<∞ in the F-case), 0<q≤∞ and the weight w(x)∈W. 相似文献
2.
E. G. Goluzina 《Journal of Mathematical Sciences》1998,89(1):958-966
Let TR be the class of functions
that are regular and typically real in the disk E={z:⋱z⋱<1}. For this class, the region of values of the system {f(z0), f(r)} for z0 ∈ ℝ, r∈(-1,1) is studied. The sets Dr={f(z0):f∈TR, f(r)=a} for −1≤r≤1 and Δr={(c2, c3): f ∈ TR, −f(−r)=a} for 0<r≤1 are found, where aε(r(1+r)−2, r(1−r)−2) is an arbitrary fixed number. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 69–79. 相似文献
3.
Pascale Vitse 《Rendiconti del Circolo Matematico di Palermo》2004,53(2):283-312
For Banach space operatorsT satisfying the Tadmor-Ritt condition ‖(zI−T)−1‖≤C|z−1|−1, |z|>1, we show how to use the Riesz turndown collar theorem to estimate sup
n≥0‖T
n‖. A similar estimate is shown for lim sup
n
‖T
n‖ in terms of the Ritt constantM=lim sup
z→1‖(1−z)(zI−T)−1‖. We also obtain an estimate of the functional calculus for these operators proving, in particular, that ‖f(T)‖≤C
q‖f‖
Mult
, where ‖·‖
Mult
stands for the multiplier norm of the Cauchy-Stieltjes integrals over a Lusin type cone domain depending onC and a parameterq, 0<q<1.
Notation.D denotes the open unit disc of the complex plane,D={z∈ℂ:|z|<1}, andT={z∈ℂ:|z|=1} is the unit circle.H
∞ is the Banach algebra of bounded analytic functions onD equipped with the supremum norm ‖.‖∞. 相似文献
4.
Abdelbaki Boutabaa 《manuscripta mathematica》1990,67(1):251-269
We study meromorphic functions in all ℂp or in a disc of ℂp. Using some properties of the valuation polygon notion, we show
p-adic results perfectly analogous to those of Nevanlinna in the complex case.
As an application we prove the p-adic analogue of Malmquist-Yosida Theorem: Let m∈ℕ and R(x.y)∈ℂp(x,y). If the differential
equation: (dy/dx)m=R(x,y), m∈ℕ, has a non rational meromorphic solution in all ℂp, then R(x,y) is a polynomial in y of degree ≤2m.
相似文献
5.
R. S. Yulmukhametov 《Mathematical Notes》1997,62(2):260-267
We consider the problem of approximating a given plurisubharmonic function by smooth plurisubharmonic functions. We propose
a new constructive approximation method that permits one to obtain more detailed information about the approximating functions.
Thus a functionu ∈ PSH(ℂ
n
) having finite growth order can be approximated by smooth functionsv ∈ PSH(ℂ
n
) so that the difference |v−u| has almost logarithmic growth (Theorem 2). It can also be approximated so that the difference |v−u| has a power-law growth; in this case, however, power-law estimates on |gradv| appear (Theorem 3).
Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 312–320, August, 1997.
Translated by I. P. Zvyagin 相似文献
6.
Bao Yongguang 《分析论及其应用》1995,11(4):15-23
Let ξn −1 < ξn −2 < ξn − 2 < ... < ξ1 be the zeros of the the (n−1)-th Legendre polynomial Pn−1(x) and −1=xn<xn−1<...<x1=1, the zeros of the polynomial
. By the theory of the inverse Pal-Type interpolation, for a function f(x)∈C
[−1,1]
1
, there exists a unique polynomial Rn(x) of degree 2n−2 (if n is even) satisfying conditions Rn(f, ξk) = f (εk) (1 ⩽ k ⩽ n −1); R1
n(f,xk)=f1(xk)(1≤k≤n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation
polynomial {Rn(f, x)} (n is even) and the main result of this paper is that if f∈C
[1,1]
r
, r≥2, n≥r+2, and n is even then |R1
n(f,x)−f1(x)|=0(1)|Wn(x)|h(x)·n3−r·E2n−r−3(f(r)) holds uniformly for all x∈[−1,1], where
. 相似文献
7.
You Peng CHEN Chun Hong XIE 《数学学报(英文版)》2006,22(5):1297-1304
This paper deals with the strongly coupled parabolic system ut = v^m△u, vt = u^n△v, (x, t) ∈Ω × (0,T) subject to nonlinear boundary conditions 偏du/偏dη = u^αv^p, 偏du/偏dη= u^qv^β, (x, t) ∈ 偏dΩ × (0, T), where Ω 包含 RN is a bounded domain, m, n are positive constants and α,β, p, q are nonnegative constants. Global existence and nonexistence of the positive solution of the above problem are studied and a new criterion is established. It is proved that the positive solution of the above problem exists globally if and only if α 〈 1,β 〈 1 and (m +p)(n + q) ≤ (1 - α)(1 -β). 相似文献
8.
It is well known that the number of isolated singular points of a hypersurface of degree d in ℂPm does not exceed the Arnol’d number Am(d), which is defined in combinatorial terms. In the paper it is proved that if b
m−1
±
(d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂPm, then the inequality Am(d)<min{b
m−1
+
(d), b
m−1
−
(d)} holds if and only if (m−5)(d−2)≥18 and (m,d)≠(7,12). The table of the Arnol’d numbers for 3≤m≤14, 3≤d≤17 and for 3≤m≤14,
d=18, 19 is given. Bibliography: 6 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 180–190.
Translated by O. A. Ivanov and N. Yu. Netsvetev. 相似文献
9.
Noga Alon 《Graphs and Combinatorics》1985,1(1):305-310
LetG=(V,E) be a graph with an initial signs(v)∈{±1} for every vertexv∈V. When a certexv becomesactive, it resets its sign tos′(v) which is the sign of the majority of its neighbors(s′(v)=1 if there is a tie).G is in astable state if,s′(v) for allv∈V. We show that for every graphG=(V,E) and every initial signs, there is a sequencev
1,v
2,...,v
r
of vertices ofG, in which no vertex appears more than once, such that ifv
i
becomes active at timei, (1≤i≤r), then after theser stepsG reaches a stable state. This proves a conjecture of Miller. We also consider some generalizations to directed graphs with
weighted edges. 相似文献
10.
E. G. Goluzina 《Journal of Mathematical Sciences》1996,79(5):1304-1307
We study the structural properties of the class Mk,λ,b(k≥2, 0≤λ≤1, b∈ℂ\{0}) of functions f(z)=z+ ... which are regular in |z|<1 and satisfy the conditions f(z)f′(z)z−1≠0 and
, where J(z)=λ(1+b−1zf″(z)/f′(z)+(1−λ)(b−1zf′(z)/f(z)+1−b−1). The value regions of some functionals on this class are found. The case λ=1 was considered in our previous paper. Bibliography:
4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 55–60.
Translated by O. A. Ivanov. 相似文献
11.
Chen Jiecheng Zhu Xiangrong 《高校应用数学学报(英文版)》2005,20(3):316-322
Given a positive Radon measure μ on R^d satisfying the linear growth condition μ(B(x,r))≤C0r^n,x∈R^d,r〉0,(1) where n is a fixed number and O〈n≤d. When d-1〈n,it is proved that if Tt,N1=0,then the corresponding maximal Calderon-Zygmund singular integral is bounded from RBMO to itself only except that it is infinite μ-a. e. on R^d. 相似文献
12.
On weighted approximation by Bernstein-Durrmeyer operators 总被引:6,自引:0,他引:6
Zhang Zhenqiu 《分析论及其应用》1991,7(2):51-64
In this paper, we consider weighted approximation by Bernstein-Durrmeyer operators in Lp[0, 1] (1≤p≤∞), where the weight function w(x)=xα(1−x)β,−1/p<α, β<1-1/p. We obtain the direct and converse theorems. As an important tool we use appropriate K-functionals.
Supported by Zhejiang Provincial Science Foundation. 相似文献
13.
S. N. M. Ruijsenaars 《Theoretical and Mathematical Physics》2006,146(1):25-33
Letting Al(x) denote the commuting analytic difference operators of elliptic relativistic Calogero-Moser type, we present and study
zero-eigenvalue eigenfunctions for the operators Al(x) − Al(−y) (with l = 1, 2,..., N and x, y ∈ ℂ
N). The eigenfunctions are products of elliptic gamma functions. They are invariant under permutations of x1,..., xN and y1,..., yN and under interchange of the step-size parameters.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 31–41, January, 2006. 相似文献
14.
In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 <α≤ 1). 相似文献
15.
Best linear methods for the approximation of functions of the Bergman class by algebraic polynomials
V. V. Savchuk 《Ukrainian Mathematical Journal》2006,58(12):1904-1915
On concentric circles T
ϱ
= {z ∈ ℂ: ∣z∣ = ϱ}, 0 ≤ ϱ < 1, we determine the exact values of the quantities of the best approximation of holomorphic functions of the Bergman
class A
p
, 2 ≤ p ≤ ∞, in the uniform metric by algebraic polynomials generated by linear methods of summation of Taylor series. For 1 ≤ p < 2, we establish exact order estimates for these quantities.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1674–1685, December, 2006. 相似文献
16.
Let ρ be a triangulation of a polygonal domain D⊂R2 with vertices V={vi:l≤i≤Nv} and RSk(D, ρ)={u∈Ck(D): ≠ T∈ρ, u/T is a rational function}. The purpose of this paper is to study the existence and construction of Cμ-rational spline functions on any triangulation ρ for CAGD. The Hermite problem Hμ(V,U)={find u∈U: Dαu(vi)=Dαf(vi),|α|≤μ} is solved by the generalized wedge function method in rational spline function family, i.e. U=RSμ. this solution needs only the knowledge of partial derivatives of order≤μ at vi. The explicit repesentations of all Cμ-GWF(generalized wedge functions)and the interpolating operator with degree of precision at least 2μ+1 for any triangulation
are given. 相似文献
17.
D. Chelkak 《Journal of Mathematical Sciences》2010,166(1):118-126
The Sturm–Liouville operators −y″ + v(x)y on [0, 1] with Dirichlet boundary conditions y(0) = y(1) = 0 are considered. For
any 1 ≤ p < ∞, a short proof of the characterization theorem for the spectral data corresponding to v ∈ Lp(0, 1) is given. Bibliography: 10 titles. 相似文献
18.
Suppose that(T
t
)t>0 is aC
0 semi-group of contractions on a Banach spaceX, such that there exists a vectorx∈X, ‖x‖=1 verifyingJ
−1(Jx)={x}, whereJ is the duality mapping fromX toP(X
*). If |<T
t
x,f>|→1, whent→+∞ for somef∈X
*, ‖f‖≤1 thenx is an eigenvector of the generatorA, associated with a purcly imaginary eigenvalue. Because of Lin's example [L], the hypothesis onx∈X is the best possible.
If the hypothesisJ
−1(Jx)={x} is not verified, we can prove that ifJx is a singleton and ifJ
−1(Jx) is weakly compact, then if |<T
t
x, f>|→1, whent→+∞ for somef∈X
*, ‖f‖≤1, there existsy∈J
−1(Jx) such thaty is an eigenvector of the generatorA, associated with a purely imaginary eigenvalue. We give also a counter-example in the case whereX is one of the spaces ℓ1 orL
1. 相似文献
19.
Pavel Shvartsman 《Journal of Geometric Analysis》2002,12(2):289-324
We prove a Helly-type theorem for the family of all m-dimensional convex compact subsets of a Banach space X. The result is
formulated in terms of Lipschitz selections of set-valued mappings from a metric space (M, ρ) into this family.
Let M be finite and let F be such a mapping satisfying the following condition: for every subset M′ ⊂ M consisting of at most
2m+1 points, the restriction F|M′ of F to M′ has a selection fM′ (i. e., fM′(x) ∈ F(x) for all x ∈ M′) satisfying the Lipschitz condition ‖ƒM′(x) − ƒM′(y)‖X ≤ ρ(x, y), x, y ∈ M′. Then F has a Lipschitz selection ƒ: M → X such that ‖ƒ(x) − ƒ(y)‖X ≤ γρ(x,y), x, y ∈ M where γ is a constant depending only on m and the cardinality of M. We prove that in general, the upper
bound of the number of points in M′, 2m+1, is sharp.
If dim X = 2, then the result is true for arbitrary (not necessarily finite) metric space. We apply this result to Whitney’s
extension problem for spaces of smooth functions. In particular, we obtain a constructive necessary and sufficient condition
for a function defined on a closed subset of
R
2
to be the restriction of a function from the Sobolev space W
∞
2
(R
2).A similar result is proved for the space of functions on
R
2
satisfying the Zygmund condition. 相似文献
20.
For β > 0 and an integer r ≥ 2, denote by [(H)\tilde]¥,br\tilde H_{\infty ,\beta }^r those 2π-periodic, real-valued functions f on ℝ, which are analytic in S
β
:= {z ∈ ℂ: |Im z| < β} and satisfy the restriction |f
(r)(z)|≤1, z ∈ S
β
. The optimal quadrature formulae about information composed of the values of a function and its kth (k = 1, ..., r − 1) derivatives on free knots for the classes [(H)\tilde]¥,br\tilde H_{\infty ,\beta }^r are obtained, and the error estimates of the optimal quadrature formulae are exactly determined. 相似文献