Regularity of Minkowski's question mark measure, its inverse and a class of IFS invariant measures

[1]  Walter Van Assche,et al.  Orthogonal polynomials for Minkowski's question mark function , 2014, J. Comput. Appl. Math..

[2]  M. Stern.  Ueber eine zahlentheoretische Funktion. , 1858 .

[3]  Paul Erdös,et al.  On Interpolation. III. Interpolatory Theory of Polynomials , 1940 .

[4]  V. Totik,et al.  Nth Root Root Asymptotic Behavior of Orthonormal Polynomials , 1990 .

[5]  S. Isola,et al.  Orderings of the rationals and dynamical systems , 2008, 0805.2178.

[6]  J. Kinney.  Note on a singular function of Minkowski , 1960 .

[7]  G. Mantica.  Wave propagation in almost-periodic structures , 1997 .

[8]  Giorgio Mantica,et al.  Minkowski's question mark measure , 2016, J. Approx. Theory.

[9]  K. Okamura.  Singularity Results for Functional Equations Driven by Linear Fractional Transformations , 2012, 1205.3632.

[10]  G. Mantica,et al.  The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics , 2007 .

[11]  Marc Kessebohmer,et al.  Fractal analysis for sets of non-differentiability of Minkowski's question mark function , 2007, 0706.0453.

[12]  Edward B. Saff,et al.  Orthogonal Polynomials from a Complex Perspective , 1990 .

[13]  Generalized Farey Trees, Transfer Operators and Phase Transitions , 2007 .

[14]  V. Totik,et al.  Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle , 1985 .

[15]  R. Strichartz.  Self-similar measures and their Fourier transforms. II , 1993 .

[16]  Giedrius Alkauskas.  Integral transforms of the Minkowski question mark function , 2008 .

[17]  Tuomas Sahlsten,et al.  Fourier transforms of Gibbs measures for the Gauss map , 2013, 1312.3619.

[18]  M. Gutzwiller.  Bernoulli sequences and trajectories in the anisotropic Kepler problem , 1977 .

[19]  D. Bessis,et al.  Orthogonal polynomials associated to almost periodic Schro¨dinger operators: a trend towards random orthogonal polynomials , 1993 .

[20]  M. Kesseböhmer,et al.  STERN–BROCOT PRESSURE AND MULTIFRACTAL SPECTRA IN ERGODIC THEORY OF NUMBERS , 2004 .

[21]  F. Mendivil.  A Generalization of IFS with Probabilities to Infinitely Many Maps , 1998 .

[23]  Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function , 2009, 0912.1039.

[24]  J. Ullman.  On the Regular Behaviour of Orthogonal Polynomials , 1972 .

[25]  Kenny,et al.  Phase transitions on strange irrational sets. , 1989, Physical review. A, General physics.

[26]  Jaume Paradís,et al.  A new light on Minkowski's? $(x)$ function , 1998 .

[27]  C. Series.  The modular surface and continued fractions , 1985 .

[28]  R. Salem.  On some singular monotonic functions which are strictly increasing , 1943 .

[29]  Guarneri,et al.  Multifractal energy spectra and their dynamical implications. , 1994, Physical review letters.

[30]  Giedrius Alkauskas.  The Minkowski question mark function: explicit series for the dyadic period function and moments , 2010, Math. Comput..

[31]  G. Mantica.  On computing Jacobi matrices associated with recurrent and Möbius iterated function systems , 2000 .

[32]  W. Assche,et al.  Sieved orthogonal polynomials and discrete measures with jumps dense in an interval , 1989 .

[33]  M. Barnsley,et al.  Iterated function systems and the global construction of fractals , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.