AbstractThe self-affine measure μMp,D corresponding toMp=2p02(p∈Z)andD=00,10,01is supported on the the generalized plane Sierpinski gasket T(Mp,D). In the present paper we show that there exist at most 3 mutually orthogonal exponential functions in L2(μMp,D), and the number 3 is the best. This generalizes several known results on the non-spectral self-affine measure problem
AbstractLet the polynomialsPn(x),n⩾1, be defned byP0(x)=0,P1(x)=1,anPn+1(x)+an−1Pn−1(x)+bnPn(x)=xPn(...
11 pages; latex2e; pas de figuresThe orthogonal polynomials with recurrence relation \[(\la_n+\mu_n-...
In this paper we solve an open problem concerning the characterization of those measurable sets Ω ⊂ ...
AbstractThe self-affine measure μM,D corresponding to the expanding integer matrixM=[p0m0p000p]andD=...
AbstractThe self-affine measure μM,D corresponding to an expanding integer matrixM=[abcd]andD={(00),...
AbstractThe self-affine measure μM,D corresponding to the expanding integer matrixM=[p0m0p000p]andD=...
AbstractThe self-affine measures μM,D corresponding to the case (i) M=pI3, D={0,e1,e2,e3} in the spa...
AbstractThe self-affine measure μM,D associated with an affine iterated function system {ϕd(x)=M−1(x...
AbstractLet μM,D be a self-affine measure associated with an expanding integer matrix M∈Mn(Z) and a ...
AbstractWe are concerned with an harmonic analysis in Hilbert spaces L2(μ), where μ is a probability...
AbstractA Borel measure μ in Rd is called a spectral measure if there exists a set Λ⊂Rd such that th...
AbstractIn the present paper we will study the spectral property of a class of self-affine measures ...
We discuss quantitative estimates of the local spectral dimension of the two-dimensional Sierpinski ...
This is a comprehensive review of the uses of potential theory in studying the spectral theory of o...
This is a comprehensive review of the uses of potential theory in studying the spectral theory of o...
AbstractLet the polynomialsPn(x),n⩾1, be defned byP0(x)=0,P1(x)=1,anPn+1(x)+an−1Pn−1(x)+bnPn(x)=xPn(...
11 pages; latex2e; pas de figuresThe orthogonal polynomials with recurrence relation \[(\la_n+\mu_n-...
In this paper we solve an open problem concerning the characterization of those measurable sets Ω ⊂ ...
AbstractThe self-affine measure μM,D corresponding to the expanding integer matrixM=[p0m0p000p]andD=...
AbstractThe self-affine measure μM,D corresponding to an expanding integer matrixM=[abcd]andD={(00),...
AbstractThe self-affine measure μM,D corresponding to the expanding integer matrixM=[p0m0p000p]andD=...
AbstractThe self-affine measures μM,D corresponding to the case (i) M=pI3, D={0,e1,e2,e3} in the spa...
AbstractThe self-affine measure μM,D associated with an affine iterated function system {ϕd(x)=M−1(x...
AbstractLet μM,D be a self-affine measure associated with an expanding integer matrix M∈Mn(Z) and a ...
AbstractWe are concerned with an harmonic analysis in Hilbert spaces L2(μ), where μ is a probability...
AbstractA Borel measure μ in Rd is called a spectral measure if there exists a set Λ⊂Rd such that th...
AbstractIn the present paper we will study the spectral property of a class of self-affine measures ...
We discuss quantitative estimates of the local spectral dimension of the two-dimensional Sierpinski ...
This is a comprehensive review of the uses of potential theory in studying the spectral theory of o...
This is a comprehensive review of the uses of potential theory in studying the spectral theory of o...
AbstractLet the polynomialsPn(x),n⩾1, be defned byP0(x)=0,P1(x)=1,anPn+1(x)+an−1Pn−1(x)+bnPn(x)=xPn(...
11 pages; latex2e; pas de figuresThe orthogonal polynomials with recurrence relation \[(\la_n+\mu_n-...
In this paper we solve an open problem concerning the characterization of those measurable sets Ω ⊂ ...
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