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1.
We consider wavelet decompositions of spaces of Hermite type splines of class C1(α, β) that are defined by a 4-component vector-valued function ϕ(t) ∈ C1 (α, β) by means of a grid X (not necessarily uniform) on (α, β) ∈ ℝ1 (the special case ϕ(t)def = (1, t, t2,t3)T corresponds to cubic Hermite splines). The basis wavelets obtained are compactly supported. The decomposition and reconstruction
formulas are given. Bibliography: 8 titles.
__________
Translated from Problemy Matematicheskogo Analiza, No. 35, 2007, pp. 33–46 相似文献
2.
M. Felten 《Acta Mathematica Hungarica》2008,118(3):227-263
Lubinsky and Totik’s decomposition [11] of the Cesàro operators σ
n
(α,β)
of Jacobi expansions is modified to prove uniform boundedness in weighted sup norms, i.e., ‖w
(a,b)
σ
n
(α,β)
‖∞ ≦ C‖w
(a,b)
f‖∞, whenever α,β ≧ −1/2 and a, b are within the square around (α/2 + 1/4, α/2 + 1/4) having a side length of 1. This approach uses only classical results from the theory of orthogonal polynomials and
various estimates for the Jacobi weights. The present paper is concerned with the main theorems and ideas, while a second
paper [7] provides some necessary estimations.
相似文献
3.
Given a graph G with characteristic polynomial ϕ(t), we consider the ML-decomposition ϕ(t) = q
1(t)q
2(t)2 ... q
m
(t)m, where each q
i
(t) is an integral polynomial and the roots of ϕ(t) with multiplicity j are exactly the roots of q
j
(t). We give an algorithm to construct the polynomials q
i
(t) and describe some relations of their coefficients with other combinatorial invariants of G. In particular, we get new bounds for the energy E(G) =
|λi| of G, where λ1, λ2, ..., λn are the eigenvalues of G (with multiplicity). Most of the results are proved for the more general situation of a Hermitian matrix whose characteristic
polynomial has integral coefficients.
This work was done during a visit of the second named author to UNAM. 相似文献
4.
Let A denote the class of functions which are analytic in |z|<1 and normalized so that f(0)=0 and f′(0)=1, and let R(α, β)⊂A
be the class of functions f such thatRe[f′(z)+αzf″(z)]>β,Re α>0, β<1. We determine conditions under which (i) f ∈ R(α1, β1), g ∈ R(α2, β2) implies that the convolution f×g of f and g is convex; (ii) f ∈ R(0, β1), g ∈ R(0, β2) implies that f×g is starlike; (iii) f≠A such that f′(z)[f(z)/z]μ-1 ≺ 1 + λz, μ>0, 0<λ<1, is starlike, and (iv) f≠A such that f′(z)+αzf″(z) ≺ 1 + λz, α>0, δ>0, is convex or starlike. Bibliography:
16 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 138–154. 相似文献
5.
Min Guohua 《分析论及其应用》1992,8(3):28-37
In this paper, the Lp-convergence of Grünwald interpolation Gn(f,x) based on the zeros of Jacobi polynomials J
n
(α,β)
(x)(−1<α,β<1) is considered. Lp-convergence (0<p<2) of Grünwald interpolation Gn(f,x) is proved for p·Max(α,β)<1. Moreover, Lp-convergence (p>0) of Gn(f,x) is obtained for −1<α,β≤0. Therefore, the results of [1] and [3–5] are improved. 相似文献
6.
As is well known the kernel of the orthogonal projector onto the polynomials of
degree n in L2(wα,β, [−1, 1]), wα,β(t) = (1 − t)α(1 + t)β, can be written in terms of Jacobi polynomials. It is shown that if the coefficients in this kernel are smoothed out by sampling
a compactly supported C∞ function then the resulting function has nearly exponential (faster than any polynomial) rate of decay away from the main
diagonal. This result is used for the construction of tight polynomial frames for L2(wα,β) with elements having almost exponential localization. 相似文献
7.
Tamar Burak 《Israel Journal of Mathematics》1973,16(4):404-417
Fort ∈ [a, b], letA(t) be the unbounded operator inH
0,p
(G) associated with an elliptic-boundary value problem that satisfies Agmon’s conditions on the rays λ=±iτ, τ ≥0. Existence and uniqueness results are obtained for weak and strict solutions of two-point problems of the type (du/dt)−A(t) u(t) =f(t),E
1(α)u (α)=u
α,E
2 (β)u (β)=u
β. Here [α, β) χ- [a, b],E
1 (α) andE
2 (β) are spectral projections associated withA(α) andA(β) respectively, andA(α)E
1 (α) and =A (β)E
2 (β) are infinitesimal generators of analytic semigroups. WhenA(t) andf(t) are analytic in a convex, complex neighborhoodO of [a, b] we show that for someθ
i
,i=1,2, any solution ofdu/dt =A(t)u (t)=f(t) in [a, b] is analytic and satisfies the above equation in the setO∩{t; t ≠ a, t ≠ b, | arg (t −a) | <θ
1, | arg (b −t) |θ
2}.
Research partially supported by N. N. F. grant at Brandeis University. 相似文献
8.
El Maati Ouhabaz 《Semigroup Forum》1998,57(3):305-314
m
σ/|α|=|β|=m Dα(a
αβDβ) is a higher order degenerate-elliptic operator on L2(RN) and V ∈ L1(RN) we show in particular that s(λ) > 0 for all λ > 0 provided that ∫RN V(x)dx≥ 0, V not equivalent to 0 and N ≤ 2m. 相似文献
9.
For given analytic functions ϕ(z) = z + Σ
n=2∞ λ
n
z
n
, Ψ(z) = z + Σ
n=2∞ μ with λ
n
≥ 0, μ
n
≥ 0, and λ
n
≥ μ
n
and for α, β (0≤α<1, 0<β≤1), let E(φ,ψ; α, β) be of analytic functions ƒ(z) = z + Σ
n=2∞
a
n
z
n
in U such that f(z)*ψ(z)≠0 and
for z∈U; here, * denotes the Hadamard product. Let T be the class of functions ƒ(z) = z - Σ
n=2∞|a
n
| that are analytic and univalent in U, and let E
T
(φ,ψ;α,β)=E(φ,ψ;α,β)∩T. Coefficient estimates, extreme points, distortion properties, etc. are determined for the class E
T
(φ,ψ;α,β) in the case where the second coefficient is fixed. The results thus obtained, for particular choices of φ(z) and ψ(z), not only generalize various known results but also give rise to several new results.
University of Bahrain, Isa Town, Bahrain. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1162–1170,
September, 1997. 相似文献
10.
Let (S)⊄L
2(S′(∔),μ)⊄(S)* be the Gel'fand triple over the white noise space (S′(∔),μ). Let (e
n
,n>-0) be the ONB ofL
2(∔) consisting of the eigenfunctions of the s.a. operator
. In this paper the Euler operator Δ
E
is defined as the sum
, where ∂
i
stands for the differential operatorD
e
i. It is shown that Δ
E
is the infinitesimal generator of the semigroup (T
t
), where (T
t
ϕ)(x)=ϕ(e
t
x) for ϕ∈(S). Similarly to the finite dimensional case, the λ-order homogeneous test functionals are characterized by the Euler equation:
Δ
Eϕ
=λϕ. Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.
Supported by the National Natural Science Foundation of China. 相似文献
11.
Let f∈C
[−1,1]
″
(r≥1) and Rn(f,α,β,x) be the generalized Pál interpolation polynomials satisfying the conditions Rn(f,α,β,xk)=f(xk),Rn
′(f,α,β,xk)=f′(xk)(k=1,2,…,n), where {xk} are the roots of n-th Jacobi polynomial Pn(α,β,x),α,β>−1 and {x
k
″
} are the roots of (1−x2)Pn″(α,β,x). In this paper, we prove that
holds uniformly on [0,1].
In Memory of Professor M. T. Cheng
Supported by the Science Foundation of CSBTB and the Natural Science Foundatioin of Zhejiang. 相似文献
12.
A. F. Izé 《Annali di Matematica Pura ed Applicata》1973,96(1):21-39
Summary It is studied the relationship between the solutions of the linear functional differential equations(1) (d/dx) D(xt)=L(xt) and its perturbed equation(2) [(d/dx) D(xt)−G(t, xt)]= =L(xt)+F(t, xt) and is proved, under certain hypotheses which will be precised bellow that, if μ is a simple characteristic root of(1), then there exist a σ > 0 and a non zero vector a such that system(2) has a solution satisfying
where δ(t)=αd{F(t, ϕμ)+μG(t, ϕμ)+F(t, X0G(t, ϕμ))}, ϕμ(θ)=c·exp (μθ), −r⩾θ⩾0 and α, d, X0 are given constants.
Entrata in Redazione il 5 gennaio 1972. 相似文献
13.
Summary This paper is concerned with second order differential systems involving two parameters with boundary conditions specified
at three points. In particular, we consider the system y' = k(x, λ, μ)z, z' = -g(x, λ, μ)y, where k and g are real-valued
junctions defined on X: a ≤ x ≤ c, L: L1 < λ < L2, and M: M1 < μ < M2. This system is studied together with the boundary conditions α(λ, μ)y(a) - β(λ, μ)z(a)=0, γ(λ, μ)y(b) - δ(λ, μ)z(b)=0, ε1(μ)y(b) - φ1(μ)z(b)=ε2(μ)y(c) - φ2(μ)z(c), where α, β, δ, γ, εi, φi, i=1, 2, are continuous functions of the parameters. This work establishes the existence of eigenvalue pairs for the boundary
problem and the oscillatory behavior of the associated solutions. These results complement those previously obtained by the
authors and B. D. Sleeman, where boundary conditions of the ? Sturm-Liouville ? type were studied.
Entrata in Redazione il 5 dicembre 1977.
The research for this paper was supported by a University College Reasearch Grant, University of Alabama in Birmingham. 相似文献
14.
Ferenc Weisz 《分析论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded
from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H
1
#
(T×T), L1(T2)), where the Hardy space H
1
#
(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H
1
#
(T×T)⊃LlogL(T
2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces
Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too.
This research was made while the author was visiting the Humboldt University in Berlin supported by the Alexander von Humboldt
Foundation. 相似文献
15.
For the equation K(t)u
xx
+ u
tt
− b
2
K(t)u = 0 in the rectangular domain D = “(x, t)‖ 0 < x < 1, −α < t < β”, where K(t) = (sgnt)|t|
m
, m > 0, and b > 0, α > 0, and β > 0 are given real numbers, we use the spectral method to obtain necessary and sufficient conditions for the unique solvability
of the boundary value problem u(0, t) = u(1, t), u
x
(0, t) = u
x
(1, t), −α ≤ t ≤ β, u(x, β) = φ(x), u(x,−α) = ψ(x), 0 ≤ x ≤ 1. 相似文献
16.
Ferenc Weisz 《逼近论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. 相似文献
17.
S. V. Kerov 《Functional Analysis and Its Applications》2000,34(1):41-51
We study the Young lattice with the edge multiplicitiesϰ
α
(λ, ⋏) arising in the simplest Pieri formula for Jack symmetric polynomialsP
λ (x; α) with parameter α. A new proof of Stanley’s α-version of the hook formula is given. We also prove the formula
whereϕ(λ) = ∏
b∈λ
(a(b)α +l(b) + 1)−1 andc
α(b) is the α-contents of the new boxb=⋏/λ.
Partially supported by the Federal Grant Program “Integration,” No. 326.53, and by MSRI at Berkeley.
St. Petersburg Division of the V. A. Steklov Mathematical Institute. Translated from Funksional’nyi Analiz i Ego Prilozheniya,
Vol. 34, No. 1, pp. 51–64, January–March, 200.
Translated by S. V. Kerov 相似文献
18.
Jean-Pierre Levinski 《Israel Journal of Mathematics》1984,48(2-3):225-243
We consider various forms of the Conjecture of Chang. Part A constitutes an introduction. Donder and Koepke have shown that
if ρ is a cardinal such that ρ ≧ ω1, and (ρ++,ρ+↠(ρ+, ρ), then 0+ exists. We obtain the same conclusion in Part B starting from some other forms of the transfer hypothesis. As typical corollaries,
we get:
Theorem A.Assume that there exists cardinals λ, κ, such that λ ≧
K
+ ≧ω2 and (λ+, λ)↠(K
+,K. Then 0+ exists.
Theorem B.Assume that there exists a singularcardinal κ such that(K
+,K↠(ω1, ω0. Then 0+ exists.
Theorem C.Assume that (λ
++, λ). Then 0+ exists (also ifK=ω
0.
Remark. Here, as in the paper of Donder and Koepke, “O+ exists” is a matter of saying that the hypothesis is strictly stronger than “L(μ) exists”. Of course, the same proof could give a few more sharps overL(μ), but the interest is in expecting more cardinals, coming from a larger core model.
Theorem D.Assume that (λ
++, λ)↠(K
+, K) and thatK≧ω
1. Then 0+ exists.
Remark 2. Theorem B is, as is well-known, false if the hypothesis “κ is singular” is removed, even if we assume thatK≧ω
2, or that κ is inaccessible. We shall recall this in due place.
Comments. Theorem B and Remark 2 suggest we seek the consistency of the hypothesis of the form:K
+, K↠(ωn +1, ωn), for κ singular andn≧0. 0266 0152 V 3
The consistency of several statements of this sort—a prototype of which is (N
ω+1,N
ω)↠(ω1, ω0) —have been established, starting with an hypothesis slightly stronger than: “there exists a huge cardinal”, but much weaker
than: “there exists a 2-huge cardinal”. These results will be published in a joint paper by M. Magidor, S. Shelah, and the
author of the present paper. 相似文献
19.
The Hausdorff Centred measure of the symmetry Cantor sets 总被引:1,自引:0,他引:1
Let 0<λ≤1/3,K (λ) be the attractor of an iterated function system { ψ1,ψ2 } on the line, where ψ1 (x ) =λx, ψ2(x)=1-λ+λx, x∈ [0,1]. We call K (λ) the symmetry Cantor sets. In this paper, we obtained the exact Hausdorff Centred measure of K (λ). 相似文献
20.
The pseudorelativistic Hamiltonian
is considered under wide conditions on potentials A(x), W(x). It is assumed that a real point λ is regular for G1/2. Let G1/2(α)=G1/2−αV, where α>0, V(x)≥0, and V ∈L
d(ℝd). Denote by N(λ, α) the number of eigenvalues of G1/2(t) that cross the point λ as t increases from 0 to α. A Weyl-type asymptotics is obtained for N(λ, α) as α→∞. Bibliography:
5 titles.
To O. A. Ladyzhenskaya
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 249, 1997. pp. 102–117.
Translated by A. B. Pushnitskii. 相似文献