共查询到20条相似文献,搜索用时 31 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.
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
14.
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
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.
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
17.
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
18.
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
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