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   Spectral models for orthonormal wavelets and related algorithms; Suchanecki, Zdzislaw  ; 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 ▲] Detailed reference viewed: 153 (2 UL)Orthonormal MRA wavelets: Spectral formulas and algorithms; Suchanecki, Zdzislaw ; in International Journal of Wavelets, Multiresolution and Information Processing (2012), 10(1), Detailed reference viewed: 103 (1 UL)On Lambda transformation approach to the theory of irreversibility; Suchanecki, Zdzislaw in Bussei Kenkyu (2012), 97(3), 398-413 Detailed reference viewed: 46 (2 UL)Spectral Models for Orthonormal Wavelets and Multiresolution Analysis of L2(R); Suchanecki, Zdzislaw 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 ▲] Detailed reference viewed: 44 (0 UL)Inner functions and local shape of orthonormal wavelets; Suchanecki, Zdzislaw 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 ▲] Detailed reference viewed: 92 (0 UL)On Lambda and Time Operators: the Inverse Intertwining Problem Revisited; Suchanecki, Zdzislaw ; 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 ▲] Detailed reference viewed: 102 (0 UL)Evolution semigroups and time operators on Banach spacesSuchanecki, Zdzislaw ; in Journal of Mathematical Analysis and 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 ▲] Detailed reference viewed: 83 (1 UL)Breakdown of Time-Reversal Symmetry: Intrinsic Randomness, Time Operator, Scattering; Suchanecki, Zdzislaw 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 ▲] Detailed reference viewed: 103 (0 UL) |
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