Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 8

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

$L^q$-spectrum of the Bernoulli convolution associated with the golden ratio

100%
Lau K.-S., Ngai S.-M.
Studia Mathematica
|
1998
|
tom 131
|
nr 3
225-251
EN
Based on a set of higher order self-similar identities for the Bernoulli convolution measure for (√5-1)/2 given by Strichartz et al., we derive a formula for the $L^q$-spectrum, q >0, of the measure. This formula is the first obtained in the case where the open set condition does not hold.
2
Content available remote

Ruelle operator with nonexpansive IFS

100%
Lau K.-S., Ye Y.-L.
Studia Mathematica
|
2001
|
tom 148
|
nr 2
143-169
EN
The Ruelle operator and the associated Perron-Frobenius property have been extensively studied in dynamical systems. Recently the theory has been adapted to iterated function systems (IFS) $(X,{w_{j}}_{j=1}^{m},{p_{j}}_{j=1}^{m})$, where the $w_{j}$'s are contractive self-maps on a compact subset $X ⊆ ℝ^{d}$ and the $p_{j}$'s are positive Dini functions on X [FL]. In this paper we consider Ruelle operators defined by weakly contractive IFS and nonexpansive IFS. It is known that in such cases, positive bounded eigenfunctions may not exist in general. Our theorems give various sufficient conditions for the existence of such eigenfunctions together with the Perron-Frobenius property.
3
Content available remote

Iterated function systems with a weak separation condition

100%
Lau K.-S., Wang X.-Y.
Studia Mathematica
|
2004
|
tom 161
|
nr 3
249-268
EN
Nonoverlapping contractive self-similar iterated function systems (IFS) have been studied in great detail via the open set condition. On the other hand much less is known about IFS with overlaps. To deal with such systems, a weak separation condition (WSC) has been introduced recently [LN1]; it is weaker than the open set condition and it includes many important overlapping cases. This paper has two purposes. First, we consider the class of self-similar measures generated by such IFS; we give a necessary and sufficient condition for the self-similar measures to be absolutely continuous with respect to Hausdorff measures. This extends a result in [LNR]. As most of the known examples of the WSC involve algebraic integers (e.g., the golden ratio, integral dilation matrices) and the contraction ratios are equal, our second goal is to give new examples of self-similar IFS with the WSC and with more arbitrary contraction ratios.
4
Content available remote

Self-affine measures and vector-valued representations

81%
Deng Q.-R., He X.-G., Lau K.-S.
Studia Mathematica
|
2008
|
tom 188
|
nr 3
259-289
EN
Let A be a d × d integral expanding matrix and let $S_{j}(x) = A^{-1}(x + d_{j})$ for some $d_{j} ∈ ℤ^{d}$, j = 1,...,m. The iterated function system (IFS) ${S_{j}}_{j=1}^{m}$ generates self-affine measures and scale functions. In general this IFS has overlaps, and it is well known that in many special cases the analysis of such measures or functions is facilitated by expressing them in vector-valued forms with respect to another IFS that satisfies the open set condition. In this paper we prove a general theorem on such representation. The proof is constructive; it depends on using a tiling IFS ${ψ_{j}}_{j=1}^{l}$ to obtain a graph directed system, together with the associated probability on the vertices to form some transition matrices. As applications, we study the dimension and Lebesgue measure of a self-affine set, the $L^{q}$-spectrum of a self-similar measure, and the existence of a scaling function (i.e., an L¹-solution of the refinement equation).
5
Content available remote

Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures

81%
Lau K.-S., Wang J.-R., Chu C.-H.
Studia Mathematica
|
1995-1996
|
tom 117
|
nr 1
1-28
EN
The Choquet-Deny theorem and Deny's theorem are extended to the vector-valued case. They are applied to give a simple nonprobabilistic proof of the vector-valued renewal theorem, which is used to study the $L^p$-dimension, the $L^p$-density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.
6
Content available remote

The convolution equation of Choquet and Deny on semigroups

70%
Lau K.-S., Zeng W.-B.
Studia Mathematica
|
1990
|
tom 97
|
nr 2
115-135
7
Content available remote

On two classes of Banach spaces with uniform normal structure

60%
Gao J., Lau K.-S.
Studia Mathematica
|
1991
|
tom 99
|
nr 1
41-56
8
Content available remote

Approximation by continuous vector valued functions

40%
Lau K.-S.
Studia Mathematica
|
1980
|
tom 68
|
nr 3
291-298
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.