| 1. |
- Bock, Wolfgang, et al.
(författare)
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Stochastic quantization for the fractional Edwards measure
- 2017
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 151, s. 81-88
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Tidskriftsartikel (refereegranskat)abstract
- We prove that there exists a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion, μg , H, H∈ (0 , 1) for dH< 1. The diffusion is constructed in the framework of Dirichlet forms in infinite dimensional (Gaussian) analysis. Moreover, the process is invariant under time translations.
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| 2. |
- Dutkay, Dorin Ervin, et al.
(författare)
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On Generalized Walsh Bases
- 2019
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 163:1, s. 73-90
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Tidskriftsartikel (refereegranskat)abstract
- This paper continues the study of orthonormal bases (ONB) of L2[0, 1] introduced in Dutkay et al. (J. Math. Anal. Appl. 409(2):1128-1139, 2014) by means of Cuntz algebra ON representations on L2[0, 1]. For N = 2, one obtains the classic Walsh system. We show that the ONB property holds precisely because the ON representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal processing we find a fast generalized transform and compare this generalized transform with the classic one with respect to compression and sparse signal recovery.
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| 3. |
- Kurujyibwami, Celestin, et al.
(författare)
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Algebraic Method for Group Classification of (1+1)-Dimensional Linear Schrodinger Equations
- 2018
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : SPRINGER. - 0167-8019 .- 1572-9036. ; 157:1, s. 171-203
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Tidskriftsartikel (refereegranskat)abstract
- We carry out the complete group classification of the class of (1+1)-dimensional linear Schrodinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we compute the equivalence groupoid of the class under study and show that it is uniformly semi-normalized. More specifically, each admissible transformation in the class is the composition of a linear superposition transformation of the corresponding initial equation and an equivalence transformation of this class. This allows us to apply the new version of the algebraic method based on uniform semi-normalization and reduce the group classification of the class under study to the classification of low-dimensional appropriate subalgebras of the associated equivalence algebra. The partition into classification cases involves two integers that characterize Lie symmetry extensions and are invariant with respect to equivalence transformations.
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