共查询到20条相似文献,搜索用时 406 毫秒
1.
Massimo Cicognani 《Annali dell'Universita di Ferrara》1987,33(1):259-292
Riassunto Si studia il problema di Cauchy per operatori differenziali lineari del secondoordine strettamente iperbolici con coefficienti
lipschitziani rispetto al tempo. Si trovano risultati di buona positura del problema negli spazi
gli ordinari spazi di Sobolev, e risultati di propagazione della regolaritàC
∞ della soluzione.
Summary We study the Cauchy problem for linear second order strictly hyperbolic differential operators whose coefficients are assumed to be Lipschitz-continuous with respect to time. We prove results ofH ∞ andH −∞ well-posedness, the usual Sobolev spaces, and results on the propagation ofC ∞-regularity of the solution.相似文献
2.
Nikolay Moshchevitin 《Czechoslovak Mathematical Journal》2012,62(1):127-137
Let Θ = (θ
1,θ
2,θ
3) ∈ ℝ3. Suppose that 1, θ
1, θ
2, θ
3 are linearly independent over ℤ. For Diophantine exponents
$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered}$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered} 相似文献
3.
4.
Deh-phone Kung Hsing 《Annali di Matematica Pura ed Applicata》1976,109(1):235-245
Summary We consider the system(L):
, t ⩾ p, y(t)=f(t), t⩽0, where y is an n-vector and each Ai, B(t) are n × n matrices. System(L) generates a semigroup by means of Ttf(s)=y (t+s, f), f(s) ∈ BCl(− ∞, 0]. Under some hypotheses concerning the roots ofdet
where
is the Laplace transform of B(t), the asymptotic behavior of y(t) is discussed. Two typical results are: Theorem 3.1: suppose
∥B(t)∥ ɛ L1[0, ∞),
thendet
forRe λ>0 iff for every ɛ>0 there is an Mɛ>0 such that ∥Ttf∥l ⩽ ⩽ Mɛ
exp [ɛt]∥f∥l for t ⩾ 0. Corollary 3.1.1: suppose
exp [at]B(t) ∈ ∈ L1[0, ∞) for some a>0 anddet
forRe λ>−a. Then the solution of(L) is exponentially asymptotically stable.
Entrata in Redazione il 21 marzo 1975.
The author is grateful to ProfessorC. Corduneanu for suggesting this problem and for many helpful discussions during the preparation of the paper. 相似文献
5.
A. N. Borodin 《Journal of Mathematical Sciences》1984,27(5):3005-3022
In this paper one considers methods which enable one to determine the distribution of certain functionals of a Brownian motion process. Among such functionals we have: the positive continuous additive functional of a Brownian motion, defined by the formula $$A\left( t \right) = \int\limits_{ - \infty }^\infty {\hat t\left( {t, y} \right)dF\left( y \right),} $$ where \(\hat t\left( {t, y} \right)\) is the Brownian local time process while F(y) is a monotonically increasing right continuous function; the functional $$B\left( t \right) = \mathop {\mathop \smallint \limits_{ - \infty } }\nolimits^\infty f\left( {y,\hat t\left( {t, y} \right)} \right)dy,$$ where f(y, x) is a continuous function; and the functional $$C\left( t \right) = \mathop {\mathop \smallint \limits_0 }\nolimits^t f\left( {w\left( s \right),\hat t\left( {sr} \right)} \right)ds$$ As an application of these methods one considers some concrete functionals such that \(\hat t^{ - 1} \left( z \right) = \min \left\{ {s:\hat t\left( {s, o} \right) = z} \right\},\mathop {\mathop \smallint \limits_{ - \infty } }\nolimits^\infty \hat t^2 \left( {t, y} \right)dy,\mathop {\sup }\limits_{y \in R^1 } \hat t\left( {T, y} \right)\) , where T is an exponential random time, independent of \(\hat t\left( {t, y} \right)\) . 相似文献
6.
We prove that, under appropriate assumptions on the domain Ω and on the datumg, any optimal partition of Ω (minimizing the sum of the total perimeter and the approximation term
is finite. Finiteness result for the problem of image segmentation in Artificial Vision can be deduced.
Sunto Dimostriamo che, in opportune ipotesi sul dominio Ω e sul datog, ogni partizione ottimale di Ω (minimizzante il perimetro totale in Ω più il termine di approssimazione è finita. Se ne deducono risultati di finitezza per il problema della segmentazione di immagini in Visione Artificiale.相似文献 7.
Yu. N. Lin'kov 《Journal of Mathematical Sciences》1991,53(1):49-55
For families of probability measures (P
, )) generated by semimartingales, we consider the local density)(y, )=
t
(y, ))
t0 of a, measureP
y
with respect to the measureP
whose logarithm is the difference of a local martingale and a positive predictable increasing locally bounded process. Conditions are obtained under which the relations
and
hold, wherey
t
depends in some way ont, while
t
ast . Applications of these relations are exhibited and an example is given when the hypotheses of the theorems proved can be verified.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 48–55, 1986. 相似文献
8.
Consider the variational integral
where Ω⊂ℝ
n
andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that
. We approximateJ by a sequence of regularized functionalsJ
δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ
δ-minimizers. 相似文献
9.
D. Fortunato 《Annali di Matematica Pura ed Applicata》1979,119(1):317-331
Summary Let A=
be an elliptic differential operator inR
u, If, for |α|=l, the coefficients aα are ? nearly constant ? and, for |α|<l, they tend to zero at infinity with a certain swiftness, it is proved that A is a
Fredholm operator with indexx(A)=0 between a suitable weighted Sobolev space M contained in Wl,p (R n) and Lp(R
n, (1+|x|)lp)==
. It is shown, by counterexamples, that the above result, holds only if n>l, p>n/(n−l) and that isomorphism results can be
obtained, in general only if the coefficients aα(|α|<l) are assumed to be ? sufficiently small ? also on compact sets. Then a Sturm-Liouville type problem is studied and
a class of negative and falling off at infinity potentials V(x) is constructed in such a way that the Schr?dinger operator
H=−Δ+V(x), in L2(R
n), has a zero eigenvalue.
Sunto Sia un operatore differenziale ellittico inR n. Se, per |α|=l, i coefficienti aα sono ? quasi costanti ? e, per |α|<l, tendono a zero all'infinito con una certa rapidità, si dimostra che A è un operatore di Fredholm con indiceX(A)=0 tra un opportuno spazio di Sobolev con peso M contenuto in Wl,p(R n) ed Lp(R n, (1+|x|)lp)== . Si prova, mediante controesempi, che tale risultato è valido solo se n>l, p>n/(n−l) e che teoremi di isomorfismo si possono ottenere, in generale, solo se si assume che i coefficienti aα (|α|<l) sono ? sufficientemente piccoli ? anche su insiemi compatti. Si studia quindi un problema del tipo Sturm-Liouville e si costruisce una classe di potenziali V(x) negativi e convergenti a zero all'infinito, tali che l'operatore di Schr?dinger H=−δ+V(x) in L2(R n) abbia un autovalore nullo. Entrata in Redazione il 10 agosto 1977. Work supported by C.N.R. (G.N.A.F.A.). 相似文献 10.
Sébastien Dubernet 《Archiv der Mathematik》2006,86(5):430-436
A well known “zero-two law" shows that if
is a strongly continuous one-parameter group of bounded operators on a Banach space X, and if
then
Here we discuss analogous problems for general unital representations θ of a topological group G on a unital Banach algebra A. Let 1 be the unit of G, and I the unit element of A. We show that either
or
if, moreover, θ admits “continuous division by any positive integer”, then, either
or
Our argument also gives automatic continuity results for representations of abelian Baire groups on a separable Banach algebra
and representations of compact non abelian groups on a Banach algebra which are locally bounded and satisfy
Received: 8 June 2005; revised: 13 October 2005 相似文献
11.
T. P. Lukašenko 《Analysis Mathematica》1982,8(4):263-275
Рассматривается воп рос о представлении о ператора Гильберта и сопряжен ной функцииA-интегралом. Доказывается следую щая Теорема. Если ? - такая неотрицательная фун кция на [0, ∞), что х?1?(х) монотонно не убывает на (0, ∞) и для н екоторого Н> 0 \(\mathop \smallint \limits_H^\infty \varphi ^{ - 1} (x)dx< \infty\) , а определенная на R функ ция fε?∩?(?), то почти всюду оператор Гильберта $$\tilde f(x) = - \frac{1}{\pi }(A)\mathop \smallint \limits_0^\infty \frac{{f(x + t) - f(x - t)}}{t}dt$$ . Из данной теоремы сле дует, что для функций и з ?p, 1<р<#x221E;, оператор Гильберта и сопряженная функция представляютсяA-инте гралом. Что для функций из ?1 п одобное утверждение неверно, показывает следующа я теорема. Теорема.Существует т акая суммируемая на R ф ункция f≧0, что почти всюду $$\mathop {\lim sup}\limits_{n \to \infty } \mathop \smallint \limits_0^\infty \left[ {\frac{{f(x + t) - f(x - t)}}{t}} \right]_n dt = \infty$$ . 相似文献
12.
ON A CLASS OF BESICOVITCHFUNCTIONS TO HAVE EXACT BOX DIMENSION: A NECESSARY AND SUFFICIENT CONDITION
This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given byB(t) := ∞∑k=1 λs-2k sin(λkt),where 1 < s < 2, λk > 0 tends to infinity as k →∞ and λk satisfies λk 1/λk ≥λ> 1. The results show thatlimk→∞ log λk 1/log λk = 1is a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions.For the fractional Riemann-Liouville differential operator Du and the fractional integral operator D-v,the results show that if λ is sufficiently large, then a necessary and sufficient condition for box dimension of Graph(D-v(B)),0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)),0 < u < 2 - s, to be s uis also lim k→∞logλk 1/log λk = 1. 相似文献
13.
This paper begins with new definitions for double sequence spaces. These new definitions are constructed, in general, by combining
modulus function and nonnegative four-dimensional matrix. We use these definitions to establish inclusion theorems between
various sequence spaces such as: If A = (a
m,n,k,l
) be a nonnegative four-dimensional matrix such that
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |