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Image Compression with Schauder Bases

Zbigniew Ciesielski (2001)

Applicationes Mathematicae

As is known, color images are represented as multiple, channels, i.e. integer-valued functions on a discrete rectangle, corresponding to pixels on the screen. Thus, image compression, can be reduced to investigating suitable properties of such, functions. Each channel is compressed independently. We are, representing each such function by means of multi-dimensional, Haar and diamond bases so that the functions can be remembered, by their basis coefficients without loss of information. For, each...

Inequivalence of Wavelet Systems in L ( d ) and B V ( d )

Paweł Bechler (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces L ( d ) and B V ( d ) are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in L ( d ) is also shown.

Injectivity onto a star-shaped set for local homeomorphisms in n-space

Gianluca Gorni, Gaetano Zampieri (1994)

Annales Polonici Mathematici

We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary function...

Interior sphere property of attainable sets and time optimal control problems

Piermarco Cannarsa, Hélène Frankowska (2006)

ESAIM: Control, Optimisation and Calculus of Variations

This paper studies the attainable set at time T>0 for the control system y ˙ ( t ) = f ( y ( t ) , u ( t ) ) u ( t ) U showing that, under suitable assumptions on f, such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C1,1-regularity for boundaries of attainable sets.

Inverse Function Theorems and Jacobians over Metric Spaces

Luca Granieri (2014)

Analysis and Geometry in Metric Spaces

We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.

Isomorphisms of AC(σ) spaces

Ian Doust, Michael Leinert (2015)

Studia Mathematica

Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if AC(σ₁) is algebra isomorphic to AC(σ₂) then σ₁ is homeomorphic to σ₂. The converse however is false. In a positive direction we show that the converse implication does hold if the sets σ₁ and σ₂ are confined to a restricted collection of compact sets, such as the set of all simple polygons.

Iterated quasi-arithmetic mean-type mappings

Paweł Pasteczka (2016)

Colloquium Mathematicae

We work with a fixed N-tuple of quasi-arithmetic means M , . . . , M N generated by an N-tuple of continuous monotone functions f , . . . , f N : I (I an interval) satisfying certain regularity conditions. It is known [initially Gauss, later Gustin, Borwein, Toader, Lehmer, Schoenberg, Foster, Philips et al.] that the iterations of the mapping I N b ( M ( b ) , . . . , M N ( b ) ) tend pointwise to a mapping having values on the diagonal of I N . Each of [all equal] coordinates of the limit is a new mean, called the Gaussian product of the means M , . . . , M N taken on b. We effectively...

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