APPLICATION OF HARMONIC ANALYSIS METHODS TO SINGULAR INTEGRALS AND CONVEX SEMI-NORMS, INTERPOLATION THEOREMS

2020 ◽  
Vol 13 (1) ◽  
pp. 1-27
Author(s):  
Mykola Ivanovich Yaremenko
Keyword(s):  
Harmonic Analysis ◽  
Singular Integrals ◽  
Analysis Methods

scholarly journals Modeling of the physical selenocentric surface using modern satellite observations and harmonic analysis methods

2018 ◽  
Vol 1038 ◽  
pp. 012003 ◽  
Author(s):  
A O Andreev ◽  
N Y Demina ◽  
Y A Nefedyev ◽  
S A Demin ◽  
A A Zagidullin
Keyword(s):  
Harmonic Analysis ◽  
Satellite Observations ◽  
Analysis Methods

scholarly journals Norm variation of ergodic averages with respect to two commuting transformations

2017 ◽  
Vol 39 (3) ◽  
pp. 658-688 ◽  
Author(s):  
POLONA DURCIK ◽  
VJEKOSLAV KOVAČ ◽  
KRISTINA ANA ŠKREB ◽  
CHRISTOPH THIELE
Keyword(s):  
Harmonic Analysis ◽  
Hilbert Transform ◽  
Singular Integrals ◽  
Quantitative Result ◽  
Square Function ◽  
Two Dimensional ◽  
Ergodic Averages ◽  
Multilinear Singular Integrals

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.

scholarly journals Three-Dimensional Texture Analysis After Bunge and Roe: Correspondence Between the Respective Mathematical Techniques

1982 ◽  
Vol 5 (2) ◽  
pp. 95-125 ◽  
Author(s):  
C. Esling ◽  
E. Bechler-Ferry ◽  
H. J. Bunge
Keyword(s):  
Harmonic Analysis ◽  
Texture Analysis ◽  
Series Expansion ◽  
Three Dimensional ◽  
Analysis Methods ◽  
Mathematical Techniques

Bunge's and Roe's three-dimensional texture analysis methods, although both founded on harmonic analysis, show some differences between the various mathematical techniques used.This paper establishes the correspondence relation between the respective mathematical techniques allowing one to compare works done in either variant. Taking the latest developments in three dimensional texture analysis into account, the correspondence relations hold for the odd degrees l as well as for the even ones.Finally numerical tables give the extension of the symmetry coefficients B:l4mμ (after Bunge) and R4nμl (after Roe) to all the degrees l of the series expansion, even and odd, including l = 34.

scholarly journals Adaptation of Classical Tidal Harmonic Analysis to Nonstationary Tides, with Application to River Tides

2013 ◽  
Vol 30 (3) ◽  
pp. 569-589 ◽  
Author(s):  
Pascal Matte ◽  
David A. Jay ◽  
Edward D. Zaron
Keyword(s):  
Time Series ◽  
Harmonic Analysis ◽  
River Flow ◽  
Water Levels ◽  
Spectral Lines ◽  
Noise Model ◽  
Analysis Tool ◽  
Tidal Analysis ◽  
Nonstationary Signals ◽  
Analysis Methods

Abstract One of the most challenging areas in tidal analysis is the study of nonstationary signals with a tidal component, as they confront both current analysis methods and dynamical understanding. A new analysis tool has been developed, NS_TIDE, adapted to the study of nonstationary signals, in this case, river tides. It builds the nonstationary forcing directly into the tidal basis functions. It is implemented by modification of T_TIDE; however, certain concepts, particularly the meaning of a constituent and the Rayleigh criterion, are redefined to account for the smearing effects on the tidal spectral lines by nontidal energy. An error estimation procedure is included that constructs a covariance matrix of the regression coefficients, based on either an uncorrelated or a correlated noise model. The output of NS_TIDE consists of time series of subtidal water levels [mean water level (MWL)] and tidal properties (amplitudes and phases), expressed in terms of external forcing functions. The method was tested using records from a station on the Columbia River, 172 km from the ocean entrance, where the tides are strongly altered by river flow. NS_TIDE hindcast explains 96.4% of the signal variance with a root-mean-square error of 0.165 m obtained from 288 parameters, far better than traditional harmonic analysis (38.5%, 0.604 m, and 127 parameters). While keeping the benefits of harmonic analysis, its advantages compared to existing tidal analysis methods include its capacity to distinguish frequencies within tidal bands without losing resolution in the time domain or data at the endpoints of the time series.

Comparative evaluation of simulation ways of the economic time series with periodic oscillations

2017 ◽  
Vol 31 (2) ◽  
pp. 181-187
Author(s):  
Y. М. Protasov ◽  
V. М. Yurov
Keyword(s):  
Time Series ◽  
Computer Simulation ◽  
Harmonic Analysis ◽  
Comparative Evaluation ◽  
Economic Time Series ◽  
Periodic Oscillations ◽  
Analysis Methods ◽  
Economic Time

Three ways of computer simulation of economic time series with periodic oscillations are compared in accordance with the criteria of accuracy and informativeness. The ways implement the harmonic analysis methods, however, the often used restriction on the length of the series is not used in this case. For example, the time series of quarterly sales volumes of the company for the last 7 years are given.

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