Harmonic Analysis: Smooth and Non-smooth
Palle E. T. Jorgensen
- Vol. 128
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The article was published on 2018-10-30 and is currently open access. It has received 7 citations till now. The article focuses on the topics: Harmonic analysis.read more
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Decomposition of Gaussian processes, and factorization of positive definite kernels
Palle E. T. Jorgensen,Feng Tian +1 more
TL;DR: In this article, the authors established a duality for two factorization questions, one for general positive definite (p.d.) kernels, and the other for Gaussian processes, for which the analytic data which determine the variety of factorizations for a given p.d. kernel is the same as that which yield factorization for a Gaussian process.
Journal ArticleDOI
The maximal cardinality of $$\mu _{M,D}$$μM,D-orthogonal exponentials on the spatial Sierpinski gasket
Qi Wang,Jian-Lin Li +1 more
TL;DR: In this paper, the maximal cardinality of the four-element orthogonal exponentials on the Sierpinski gasket was shown to be maximal in the class of exponential functions.
Journal ArticleDOI
Non-standard analysis for fractal calculus
Journal ArticleDOI
Harmonic analysis of network systems via kernels and their boundary realizations
Palle E. T. Jorgensen,James Tian +1 more
TL;DR: New tools for realizations and transforms of positive definite kernels (p.d.) of infinite network/graph models, a duality for operators and frames, optimization, Karhunen–Loève expansions, and factorizations are introduced.
Posted Content
Decomposition of Gaussian processes, and factorization of positive definite kernels
Palle E. T. Jorgensen,Feng Tian +1 more
TL;DR: In this paper, the authors established a duality for two factorization questions, one for general positive definite (p.d) kernels, and the other for Gaussian processes, which was stated via Ito-integration.
References
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A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Journal ArticleDOI
Orthonormal bases of compactly supported wavelets
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
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Theory of Reproducing Kernels.
TL;DR: In this paper, a short historical introduction is given to indicate the different manners in which these kernels have been used by various investigators and discuss the more important trends of the application of these kernels without attempting, however, a complete bibliography of the subject matter.
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Stochastic differential equations and diffusion processes
TL;DR: In this article, Stochastic Differential Equations and Diffusion Processes are used to model the diffusion process in stochastic differential equations. But they do not consider the nonlinearity of diffusion processes.