scholarly journals Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^p$ boundedness

2016 ◽  
Vol 369 (4) ◽  
pp. 2493-2519 ◽  
Author(s):  
Shaoming Guo
Keyword(s):  
Hilbert Transform ◽  
Vector Fields ◽  
Measurable Vector

scholarly journals Flows of measures generated by vector fields

2018 ◽  
Vol 148 (4) ◽  
pp. 773-818
Author(s):  
Emanuele Paolini ◽  
Eugene Stepanov
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Borel Measure ◽  
Weak Sense ◽  
Positive Borel Measure ◽  
Smooth Structure ◽  
Smooth Vector ◽  
Integral Curves ◽  
The Given ◽  
Measurable Vector

The scope of the paper is twofold. We show that for a large class of measurable vector fields in the sense of Weaver (i.e. derivations over the algebra of Lipschitz functions), called in the paper laminated, the notion of integral curves may be naturally defined and characterized (when appropriate) by an ordinary differential equation. We further show that for such vector fields the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure ‘flows along’ the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

Parallel Computation of Complex Antennas around the Coated Object Using Iterative Vector Fields Technique

2014 ◽  
Vol E97.C (7) ◽  
pp. 661-669
Author(s):  
Ying YAN ◽  
Xunwang ZHAO ◽  
Yu ZHANG ◽  
Changhong LIANG ◽  
Zhewang MA
Keyword(s):  
Parallel Computation ◽  
Vector Fields
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