共查询到20条相似文献,搜索用时 31 毫秒
1.
J. Knežević-Miljanović 《Differential Equations》2011,47(1):149-152
We prove a number of theorems on asymptotic properties of solutions of the equation y″+x
a
y
σ
= 0, σ < 0. First, we prove the absence of solutions on (x
1, +∞) for some values of the parameters a and σ; after that, we obtain asymptotic formulas for solutions defined on (x
0, +∞). 相似文献
2.
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
3.
E. Preissmann 《Aequationes Mathematicae》1987,32(1):195-212
We solve independently the equations 1/θ(x)θ(y)=ψ(x)−ψ(y)+φ(x−y)/θ(x−y) and 1/θ(x)θ(y)=σ(x)−σ(y)/θ(x−y)+τ(x)τ(y), τ(0)=0. In both cases we find θ2=aθ4+bθ2+c. We deduce estimates for the spectral radius of a matrix of type(1/θ(x
r
−x
s
)) (the accent meaning that the coefficients of the main diagonal are zero) and we study the case where thex
r
are equidistant.
Dédié to à Monsieur le Professeur Otto Haupt à l'occasion de son cententiare avec les meilleurs voeux 相似文献
4.
Julio Delgado 《Integral Equations and Operator Theory》2010,68(1):61-74
Let Ω be a second countable topological space and μ be a σ−finite measure on the Borel sets M{\mathcal{M}}. Let T be a nuclear operator on Lp(W,M,m){L^p({\Omega},{\mathcal{M}},\mu) }, 1 < p < ∞, in this work we establish a formula for the trace of T. A preliminary trace formula is established applying the general theory of traces on operator ideals introduced by Pietsch
and a characterization of nuclear operators for σ−finite measures. We also use the Doob’s maximal theorem for martingales with the purpose of studying the kernel k(x, y) of T on the diagonal. 相似文献
5.
R. Warlimont 《manuscripta mathematica》1991,71(1):197-221
The quantities ψ(x, y), ϕ(x, y) which denote the number of positive integers ≤x without prime divisors >y,<y respectively as well as the concept of a set of multiples within ℕ together with many wellknown results on these have their
counterpart in arithmetical semigroups. 相似文献
6.
In this paper, we investigate the a.s. asymptotic behavior of the solution of the stochastic differential equation dX(t) = g(X(t)) dt + σ(X(t))dW(t), X(0) ≢ 1, where g(·) and σ(·) are positive continuous functions, and W(·) is a standard Wiener process. By means of the theory of PRV functions we find conditions on g(·), σ(·), and ϕ(·) under which ϕ(X(·)) may be approximated a.s. by ϕ(μ(·)) on {X(t) → ∞}, where μ(·) is the solution of the ordinary differential equation dμ(t) = g(μ(t)) dt with μ(0) = 1.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 445–465, October–December, 2007. 相似文献
7.
James Olsen 《Israel Journal of Mathematics》1972,11(1):1-13
The principal result of this paper is that the convex combination of two positive, invertible, commuting isometries ofL
p(X,F, μ) 1<p<+∞, one of which is periodic, admits a dominated estimate with constantp/p−1. In establishing this, the following analogue of Linderholm’s theorem is obtained: Let σ and ε be two commuting non-singular
point transformations of a Lebesgue Space with τ periodic. Then given ε>O, there exists a periodic non-singular point transformation σ′ such that σ′ commutes with τ and μ(x:σ′x≠σx}<ε. Byan approximation argument, the principal result is applied to the convex combination of two isometries ofL
p (0, 1) induced by point transformations of the form τx=x
k,k>0 to show that such convex combinations admit a dominated estimate with constantp/p−1.
Research supported in part by NSF Grant No. GP-7475. A portion of the contents of this paper is based on the author’s doctoral
dissertation written under the direction of Professor R. V. Chacon of the University of Minnesota. 相似文献
8.
We consider the existence and uniqueness of singular solutions for equations of the formu
1=div(|Du|p−2
Du)-φu), with initial datau(x, 0)=0 forx⇑0. The function ϕ is a nondecreasing real function such that ϕ(0)=0 andp>2.
Under a growth condition on ϕ(u) asu→∞, (H1), we prove that for everyc>0 there exists a singular solution such thatu(x, t)→cδ(x) ast→0. This solution is unique and is called a fundamental solution. Under additional conditions, (H2) and (H3), we show the
existence of very singular solutions, i.e. singular solutions such that ∫|x|≤r
u(x,t)dx→∞ ast→0. Finally, for functions ϕ which behave like a power for largeu we prove that the very singular solution is unique. This is our main result.
In the case ϕ(u)=u
q, 1≤q, there are fundamental solutions forq<p*=p-1+(p/N) and very singular solutions forp-1<q<p*. These ranges are optimal.
Dedicated to Professor Shmuel Agmon 相似文献
9.
Yu. K. Sabitova 《Russian Mathematics (Iz VUZ)》2009,53(12):41-49
We consider the equation y
m
u
xx
− u
yy
− b
2
y
m
u = 0 in the rectangular area {(x, y) | 0 < x < 1, 0 < y < T}, where m < 0, b ≥ 0, T > 0 are given real numbers. For this equation we study problems with initial conditions u(x, 0) = τ(x), u
y
(x, 0) = ν(x), 0 ≤ x ≤ 1, and nonlocal boundary conditions u(0, y) = u(1, y), u
x
(0, y) = 0 or u
x
(0, y) = u
x
(1, y), u(1, y) = 0 with 0≤y≤T. Using the method of spectral analysis, we prove the uniqueness and existence theorems for solutions to these problems 相似文献
10.
Baode Li Yinsheng Jiang Hui Cao 《分析论及其应用》2007,23(2):138-146
In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator,simply CZO On Herz space and weak Herz space.In particular,we obtain vector-valued inequalities for CZO on Lq(Rd,│x│αdμ)space,with 1<q<∞,-n<α<n(q-1),and on L1,∞(Rd,│x│αdμ)space,with -n<α<0. 相似文献
11.
We consider an operator K˚ϕ = Lϕ−: <CDU(x), Dϕ> in a Hilbert space H, where L is an Ornstein–Uhlenbeck operator, U∈W
1,4(H, μ) and μ is the invariant measure associated with L. We show that K˚ is essentially self-adjoint in the space L
2(H, ν) where ν is the “Gibbs” measure ν(dx) = Z
−:1
e
−:2U(x)
dx. An application to Stochastic quantization is given.
Received: 13 August 1998 / Revised version: 20 September 1999 / Published online: 8 August 2000 相似文献
12.
Theorem: For each 2 ≤ k < ω there is an -sentence ϕk such that
(1) ϕk is categorical in μ if μ≤ℵk−2;
(2) ϕk is not ℵk−2-Galois stable
(3) ϕk is not categorical in any μ with μ>ℵk−2;
(4) ϕk has the disjoint amalgamation property
(5) For k > 2
(a) ϕk is (ℵ0, ℵk−3)-tame; indeed, syntactic first-order types determine Galois types over models of cardinality at most ℵk−3;
(b) ϕk is ℵm-Galois stable for m ≤ k − 3
(c) ϕk is not (ℵk−3, ℵk−2).
The first author is partially supported by NSF grant DMS-0500841. 相似文献
13.
Given a complete separable σ-finite measure space (X,Σ, μ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp (X,Σ, μ) where1<p<∞. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if(X,Σ, μ) is not purely atomic, then the unconditional basis constant of our basis is (max(p, q) −1). We derive a fast algorithm to compute the coefficients. 相似文献
14.
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A
1
TA
2
−1 and ϕ(T) = A
2
TA
1
−1 for some bijective bounded linear operators A
1; A
2 of X onto Y, or of the form φ(T) = B
1
T*B
2
−1 and ϕ(T) = B
2
T*B
−1 for some bijective bounded linear operators B
1;B
2 of X* onto Y.
相似文献
15.
To each function ϕ˜(ω) mapping the upper complex half plane ?+ into itself such that the coefficient of ω in the Nevanlinna integral representation is one, we associate the kernel p(y, dx) of a Markov chain on ℝ by
The aim of this paper is to study this chain in terms of the measure μ appearing in the Nevanlinna representation of ϕ˜(ω).
We prove in particular three results. If x
2 is integrable by μ, a law of large numbers is available. If μ is singular, i.e. if ϕ˜ is an inner function, then the operator P on L
∞(ℝ) for the Lebesgue measure is the adjoint of T defined on L
1(ℝ) by T(f)(ω) = f(ϕ(ω)), where ϕ is the restriction of ϕ˜ to ℝ. Finally, if μ is both singular and with compact support, we give a necessary
and sufficient condition for recurrence of the chain.
Received: 24 April 1998 / Revised version: 13 March 2000 / Published online: 20 October 2000 相似文献
16.
H. Stetkær 《Aequationes Mathematicae》1997,54(1-2):144-172
Summary We produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = Σ
I
2
=1
g
l
(x)h
l
(y),x, y∈G, where the functionsf,g
1,h
1 to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I encompasses classical functional equations like d’Alembert’s, Wilson’s first generalization of it, Jensen’s equation and
the quadratic equation. We solve these equations, the equation for symmetric second differences in product form and similar
functional equations for a general involution σ. 相似文献
17.
The hypergeometric function type I distribution with the pdf proportional to x
ν−1(1−x)
γ−1
2
F
1(α,β;γ;1−x), 0<x<1 occurs as the distribution of the product of two independent beta variables. In this article, a multivariate generalization
of this distribution is defined and its properties are derived.
相似文献
18.
Z. Ditzian 《Israel Journal of Mathematics》1974,17(3):315-324
Saturation classes for the sequenceK
n
(f, x) = ∫f(x −t)dμ
n
(t) of linear operators whereK
n(f, x) is of the limited oscillation type, that is,μ
n
(t) is monotonic fort ≠ [−Aσ
n
,Aσ
n
],σ
n
=o(1),n → ∞ and ∫t
2m
dμ
n
(t), are obtained. Examples of applications to some sequences of non-positive operators are given. 相似文献
19.
Let S ⊂ ℜn+1
be the graph of the function ϕ :[−1, 1]
n → ℜ defined by ϕ (x
1
, …, xn) = ∑
j=1
n
|xj|αj, with1<α
1
≤ … ≤ αn, let σ the Euclidean area measure on S. In this article we study the Lp − Lq boundedness of convolution operators with the singular Borel measure on Rn+1
given by μ (E)=σ (E ∩ S) 相似文献
20.
René L. Schilling 《Probability Theory and Related Fields》1998,112(4):565-611
Let (A,D(A)) be the infinitesimal generator of a Feller semigroup such that C
c
∞(ℝ
n
)⊂D(A) and A|C
c
∞(ℝ
n
) is a pseudo-differential operator with symbol −p(x,ξ) satisfying |p(•,ξ)|∞≤c(1+|ξ|2) and |Imp(x,ξ)|≤c
0Rep(x,ξ). We show that the associated Feller process {X
t
}
t
≥0 on ℝ
n
is a semimartingale, even a homogeneous diffusion with jumps (in the sense of [21]), and characterize the limiting behaviour
of its trajectories as t→0 and ∞. To this end, we introduce various indices, e.g., β∞
x
:={λ>0:lim
|ξ|→∞
|
x
−
y
|≤2/|ξ||p(y,ξ)|/|ξ|λ=0} or δ∞
x
:={λ>0:liminf
|ξ|→∞
|
x
−
y
|≤2/|ξ|
|ε|≤1|p(y,|ξ|ε)|/|ξ|λ=0}, and obtain a.s. (ℙ
x
) that lim
t
→0
t
−1/λ
s
≤
t
|X
s
−x|=0 or ∞ according to λ>β∞
x
or λ<δ∞
x
. Similar statements hold for the limit inferior and superior, and also for t→∞. Our results extend the constant-coefficient (i.e., Lévy) case considered by W. Pruitt [27].
Received: 21 July 1997 / Revised version: 26 January 1998 相似文献