A Modification of the Lipschitz Condition in the Newton–Kantorovich Theorem

2016 ◽  
Vol 35 (3) ◽  
pp. 309-331
Author(s):  
José Antonio Ezquerro ◽  
Miguel Angel Hernández-Verón
Keyword(s):  
Lipschitz Condition ◽  
Kantorovich Theorem

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 Existence and uniqueness regions for solutions of nonlinear equations

1978 ◽  
Vol 19 (2) ◽  
pp. 277-282 ◽  
Author(s):  
A.L. Andrew
Keyword(s):  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Kantorovich Theorem ◽  
Potential Applications ◽  
Uniqueness Theory

A refinement of the Newton-Kantorovich Theorem, which has many-potential applications in existence - uniqueness theory, is used to strengthen a result of Lancaster and Rokne concerning existence and uniqueness regions for zeros of operator polynomials.

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).

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