scholarly journals A lower lipschitz condition for the stable subordinator

1971 ◽  
Vol 17 (1) ◽  
pp. 23-32 ◽  
Author(s):  
John Hawkes
Keyword(s):  
Lipschitz Condition ◽  
Stable Subordinator

Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

scholarly journals Lipschitz continuity of spectral measures

1999 ◽  
Vol 59 (3) ◽  
pp. 369-373
Author(s):  
Werner J. Ricker
Keyword(s):  
Banach Space ◽  
Lipschitz Condition ◽  
Lipschitz Continuity ◽  
Analogous Result ◽  
Spectral Measures ◽  
Scalar Type ◽  
Algebra Of Sets

A characterisation is given of all (finitely additive) spectral measures in a Banach space (and defined on an algebra of sets) which satisfy a Lipschitz condition. This also corrects (slightly) an analogous result in the more specialised setting of resolutions of the identity of scalar-type spectral operators (due to C.A. McCarthy).

ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450007
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Lipschitz Condition ◽  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Geometric Model ◽  
Semilocal Convergence ◽  
Convergence Result ◽  
Numer Anal ◽  
The One

We present a semilocal convergence analysis of Newton's method for sections on Riemannian manifolds. Using the notion of a 2-piece L-average Lipschitz condition introduced in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] in combination with the weaker center 2-piece L1-average Lipschitz condition given by us in this paper, we provide a tighter convergence analysis than the one given in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] which in turn has improved the works in earlier studies such as [R. L. Adler, J. P. Dedieu, J. Y. Margulies, M. Martens and M. Shub, Newton's method on Riemannian manifolds and a geometric model for the human spine, IMA J. Numer. Anal.22 (2002) 359–390; F. Alvarez, J. Bolte and J. Munier, A unifying local convergence result for Newton's method in Riemannian manifolds, Found. Comput. Math.8 (2008) 197–226; J. P. Dedieu, P. Priouret and G. Malajovich, Newton's method on Riemannian manifolds: Covariant α-theory, IMA J. Numer. Anal.23 (2003) 395–419].

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