A class of Gaussian processes with fractional spectral measures

@article{Alpay2011ACO,
  title={A class of Gaussian processes with fractional spectral measures},
  author={Daniel Alpay and Palle E. T. Jorgensen and David Levanony},
  journal={Journal of Functional Analysis},
  year={2011},
  volume={261},
  pages={507-541}
}
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References

SHOWING 1-10 OF 43 REFERENCES
White noise based stochastic calculus associated with a class of Gaussian processes
Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values
Stochastic Integrals and Evolution Equations with Gaussian Random Fields
The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic
Lectures on White Noise Functionals
White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise
Affine Systems: Asymptotics at Infinity for Fractal Measures
Abstract We study measures on ℝd which are induced by a class of infinite and recursive iterations in symbolic dynamics. Beginning with a finite set of data, we analyze prescribed recursive iteration
FOURIER SERIES ON FRACTALS: A PARALLEL WITH WAVELET THEORY
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces L 2 (µ) with measures µ arising from iterated function systems (IFS). This includes equilibrium
Harmonic Analysis and Fractal Limit-Measures Induced by Representations of a Certain C*-Algebra
We describe a class of measurable subsets Ω in Rd such that L2(Ω) has an orthogonal basis of frequencies eλ(x) = ei2πλ · x(x ∈ Ω) indexed by λ ∈ Λ ⊂ Rd. We show that such spectral pairs (Ω, Λ) have a
ESTIMATES ON THE SPECTRUM OF FRACTALS ARISING FROM AFFINE ITERATIONS
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality, Classical harmonic analysis is typically
Analysis of Fractals, Image Compression, Entropy Encoding, Karhunen-Loève Transforms
TLDR
The purpose of this paper is to show that algorithms in a diverse set of applications may be cast in the context of relations on a finite set of operators in Hilbert space, and to introduce a diagionalization procedure in Karhunen-Loève analysis.
...
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