On the joint spectral radius of matrices of order 2 with equal spectral radius

Mößner, Bernhard

doi:10.1007/s10444-009-9130-y

Cited by 6 publications

(1 citation statement)

References 14 publications

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“…In general the joint spectral radius is difficult to compute exactly, even for sets of just two matrices. While much work has been done for the 2 × 2 case (see Mössner [22] and the references therein), there are few known examples for larger matrices. For our set Σ = {E, F }, however, it is possible to show through a sequence of steps that ρ(Σ) = √ α, and this will give the upper bound in Theorem 1.3.…”

Section: Flexible Case: Proof Of the Upper Boundmentioning

confidence: 99%

Hausdorff dimension of level sets of generalized Takagi functions

Allaart

2014

Math. Proc. Camb. Phil. Soc.

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This paper examines level sets of two families of continuous, nowhere differentiable functions (one a subfamily of the other) defined in terms of the "tent map". The well-known Takagi function is a special case. Sharp upper bounds are given for the Hausdorff dimension of the level sets of functions in these two families. Furthermore, the case where a function f is chosen at random from either family is considered, and results are given for the Hausdorff dimension of the zero set and the set of maximum points of f.Comment: 34 pages, 5 figures. The statement of Theorem 1.1 was expanded and various improvements to the presentation were mad

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Section: Flexible Case: Proof Of the Upper Boundmentioning

confidence: 99%

Hausdorff dimension of level sets of generalized Takagi functions

Allaart

2014

Math. Proc. Camb. Phil. Soc.

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Palindromic Matrices of Order Two and Three-Point Subdivision Schemes

Dubuc

2012

Constr Approx

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Régularité höldérienne des schémas de subdivision et des fonctions vectorielles d’échelle

Dubuc

2015

Ann. Math. Québec

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Nous reprenons le modèle de Buhmann et de Micchelli de schémas périodiques de subdivision à une variable. À chacun de ces schémas, sont associées deux équations fonctionnelles donnant lieu à la notion de fonction vectorielle d'échelle. L'étude de la régularité holdérienne des schémas de subdivision se réduit alors à celle de la régularité des fonctions vectorielles d'échelle. L'existence d'une solution de classe C m aux deux équations fonctionnelles et la valeur de la régularité holdérienne de la solution sont reliées à un rayon spectral conjoint d'opérateurs extraits de la matrice de subdivision et restreints à un sous-espace vectoriel approprié. Mots-clés Opérateur de subdivision · Fonction d'échelle · HöldérienAbstract We take up the class of periodic onedimensional subdivision schemes as defined by Buhmann and Micchelli. To each scheme are associated two functional equations giving rise to the notion of vector scaling function. The study of Hölder regularity of a subdivision scheme is then reduced to the analysis of the regularity of scaling vectors. The existence of a solution of class C m to both functional equations and the value of its Hölder regularity are related to the joint spectral radius of operators taken from the subdivision matrix that are restricted to a suitable vector subspace.

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On the joint spectral radius of matrices of order 2 with equal spectral radius

Abstract: We provide explicit formulas for the joint spectral radius of certain classes of pairs of real matrices of order 2 with equal spectral radius.

Cited by 6 publications

References 14 publications

Hausdorff dimension of level sets of generalized Takagi functions

Hausdorff dimension of level sets of generalized Takagi functions

Palindromic Matrices of Order Two and Three-Point Subdivision Schemes

Régularité höldérienne des schémas de subdivision et des fonctions vectorielles d’échelle

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