References of "Gómez-Cubillo, Fernando"
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See detailSpectral models for orthonormal wavelets and related algorithms
Gómez-Cubillo, Fernando; Suchanecki, Zdzislaw UL; Villullas, S.

in Journal of Physics: Conference Series (2014), 490

This work presents new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces are in the core of ... [more ▼]

This work presents new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces are in the core of the structure of these families. The new algorithms focus on the local shape of the wavelets, a property making them especially useful for pattern recognition. [less ▲]

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See detailOrthonormal MRA wavelets: Spectral formulas and algorithms
Gómez-Cubillo, Fernando; Suchanecki, Zdzislaw UL; Villullas, S.

in International Journal of Wavelets, Multiresolution & Information Processing (2012), 10(1),

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See detailOn Lambda transformation approach to the theory of irreversibility
Gómez-Cubillo, Fernando; Suchanecki, Zdzislaw UL

in Bussei Kenkyu (2012), 97(3), 398-413

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See detailInner functions and local shape of orthonormal wavelets
Gómez-Cubillo, Fernando; Suchanecki, Zdzislaw UL

in Applied & Computational Harmonic Analysis (2011), 30(3), 273-287

Conditions characterizing all orthonormal wavelets of L2(R) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs ... [more ▼]

Conditions characterizing all orthonormal wavelets of L2(R) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs, the so-called Haar bases, leads to new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces articulate the structure of these families. The new algorithms focus on the local shape of the wavelet. [less ▲]

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See detailSpectral Models for Orthonormal Wavelets and Multiresolution Analysis of L2(R)
Gómez-Cubillo, Fernando; Suchanecki, Zdzislaw UL

in Journal of Fourier Analysis and Applications (2011), 17(2), 191-225

Spectral representations of the dilation and translation operators on L2(R) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid ... [more ▼]

Spectral representations of the dilation and translation operators on L2(R) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes. [less ▲]

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See detailOn Lambda and Time Operators: the Inverse Intertwining Problem Revisited
Gómez-Cubillo, Fernando; Suchanecki, Zdzislaw UL; Villullas, S.

in International Journal of Theoretical Physics (2011), 50

An exact theory of irreversibility was proposed by Misra, Prigogine and Courbage, based on non-unitary similarity transformations Λ that intertwine reversible dynamics and irreversible ones. This would ... [more ▼]

An exact theory of irreversibility was proposed by Misra, Prigogine and Courbage, based on non-unitary similarity transformations Λ that intertwine reversible dynamics and irreversible ones. This would advocate the idea that irreversible behavior would originate at the microscopic level. Reversible evolution with an internal time operator have the intertwining property. Recently the inverse intertwining problem has been answered in the negative, that is, not every unitary evolution allowing such Λ-transformation has an internal time. This work contributes new results in this direction. [less ▲]

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See detailEvolution semigroups and time operators on Banach spaces
Suchanecki, Zdzislaw UL; Gomez-Cubillo, Fernando

in Journal of Mathematical Analysis & Applications (2010), 371(2), 454-464

We present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach ... [more ▼]

We present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces. [less ▲]

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See detailBreakdown of Time-Reversal Symmetry: Intrinsic Randomness, Time Operator, Scattering
Gomez-Cubillo, Fernando; Suchanecki, Zdzislaw UL

in Journal of Geometry and Symmetry in Physics (2008), 11

Misra-Prigogine-Courbage theory of irreversibility is revisited on the basis of Nagy-Foia~ dilation theory and Halmos-Helson theory of invariant sub-spaces. Universal models for intrinsically random ... [more ▼]

Misra-Prigogine-Courbage theory of irreversibility is revisited on the basis of Nagy-Foia~ dilation theory and Halmos-Helson theory of invariant sub-spaces. Universal models for intrinsically random dynamics are given as well as equivalent conditions to the existence of internal time operators, where innovation processes and Lax-Phillips scattering appear in a natural way. [less ▲]

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