scholarly journals Backward Stability of Iterations for Computing the Polar Decomposition

2012 ◽  
Vol 33 (2) ◽  
pp. 460-479 ◽  
Author(s):  
Yuji Nakatsukasa ◽  
Nicholas J. Higham
Keyword(s):  
Polar Decomposition ◽  
Backward Stability

Polar Decomposition of Wiener Measure and Schwarzian Integrals

2020 ◽  
Vol 41 (4) ◽  
pp. 709-713
Author(s):  
E. T. Shavgulidze ◽  
N. E. Shavgulidze
Keyword(s):  
Polar Decomposition ◽  
Wiener Measure

scholarly journals Unbounded Wiener–Hopf Operators and Isomorphic Singular Integral Operators

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Domenico P. L. Castrigiano
Keyword(s):  
Singular Integral ◽  
Polar Decomposition ◽  
Integral Operators ◽  
Canonical Representation ◽  
Friedrichs Extension ◽  
Finite Dimensional ◽  
Transformation Type ◽  
Rational Symbols ◽  
Shift Invariance ◽  
Densely Defined

AbstractSome basics of a theory of unbounded Wiener–Hopf operators (WH) are developed. The alternative is shown that the domain of a WH is either zero or dense. The symbols for non-trivial WH are determined explicitly by an integrability property. WH are characterized by shift invariance. We study in detail WH with rational symbols showing that they are densely defined, closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains, ranges, spectral and Fredholm points are explicitly determined. Another topic concerns semibounded WH. There is a canonical representation of a semibounded WH using a product of a closable operator and its adjoint. The Friedrichs extension is obtained replacing the operator by its closure. The polar decomposition gives rise to a Hilbert space isomorphism relating a semibounded WH to a singular integral operator of Hilbert transformation type. This remarkable relationship, which allows to transfer results and methods reciprocally, is new also in the thoroughly studied case of bounded WH.

Pol-SAR Classification Based on Generalized Polar Decomposition of Mueller Matrix

2016 ◽  
Vol 13 (4) ◽  
pp. 565-569 ◽  
Author(s):  
Hanning Wang ◽  
Zhimin Zhou ◽  
John Turnbull ◽  
Qian Song ◽  
Feng Qi
Keyword(s):  
Polar Decomposition ◽  
Mueller Matrix
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