Dense Analytic Subspaces in Fractal L 2 -spaces

@inproceedings{PEDERSENAbstract1998DenseAS,
  title={Dense Analytic Subspaces in Fractal L 2 -spaces},
  author={STEEN PEDERSENAbstract},
  year={1998}
}
  • STEEN PEDERSENAbstract
  • Published 1998
We consider self-similar measures μ with support in the interval 0 ≤ x ≤ 1 which have the analytic functions { e : n = 0, 1, 2, . . . } span a dense subspace in L (μ). Depending on the fractal dimension of μ, we identify subsets P ⊂ N0 = {0, 1, 2, . . . } such that the functions {en : n ∈ P} form an orthonormal basis for L (μ). We also give a higher-dimensional affine construction leading to self-similar measures μ with support in R . It is obtained from a given expansive ν-by-ν matrix and a… CONTINUE READING

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

239 Citations

01020'98'03'09'15
Citations per Year
Semantic Scholar estimates that this publication has 239 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
SHOWING 1-10 OF 16 REFERENCES

Fonctions harmoniques pour un operateur de transition etapplications

  • A. Raugi
  • Bull . Soc . Math . France
  • 1995

Fractals and self similarity , Indiana Univ

  • J. E. Hutchinson
  • Math . J .
  • 1995

Self - similar sets 5 : Integer matrices and fractal tilings of Rn

  • Christoph Bandt
  • Proc . Amer . Math . Soc .
  • 1994

Group - theoretic and geometric properties of multivariable Fourier series , Exposition

  • S. Pedersen
  • Math .
  • 1993

Spectral theory for Borel sets in Rn of nite measure

  • P. E. T. Jorgensen, S. Pedersen
  • J . Funct . Anal .
  • 1992

Fourier asymptotics of fractal measures

  • R. S. Strichartz
  • J . Funct . Anal .
  • 1990

Similar Papers

Loading similar papers…