Question of the domains of definition of fractional powers of accretive operators

1988 ◽  
Vol 43 (2) ◽  
pp. 129-133
Author(s):  
A. M. Gomilko
Keyword(s):  
Accretive Operators ◽  
Fractional Powers ◽  
Definition Of

scholarly journals FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE

2007 ◽  
Vol 18 (03) ◽  
pp. 281-299 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Fourier Series ◽  
Fractional Derivative ◽  
Taylor Series ◽  
Fractional Derivatives ◽  
Fractional Power ◽  
Weyl Quantization ◽  
Fractional Powers ◽  
Derivative Operator ◽  
Quantization Procedure ◽  
Definition Of

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

Gamma-convergence of Gaussian fractional perimeter

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alessandro Carbotti ◽  
Simone Cito ◽  
Domenico Angelo La Manna ◽  
Diego Pallara
Keyword(s):  
Typical Feature ◽  
Gamma Convergence ◽  
Fractional Powers ◽  
Γ Convergence ◽  
Definition Of

Abstract We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s → 1 - {s\to 1^{-}} . Our definition of fractional perimeter comes from that of the fractional powers of Ornstein–Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the Γ-limit does not depend on the dimension.

scholarly journals Approximations of Antieigenvalue and Antieigenvalue-Type Quantities

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Morteza Seddighin
Keyword(s):  
Accretive Operator ◽  
Accretive Operators ◽  
Normal Matrices ◽  
Finite Dimensional ◽  
Kantorovich Inequality ◽  
Definition Of

We will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue and Kantorovich inequality. In the second section, we approximate several antieigenvalue-type quantities for arbitrary accretive operators. Each antieigenvalue-type quantity is approximated in terms of the same quantity for normal matrices. In particular, we show that for an arbitrary accretive operator, each antieigenvalue-type quantity is the limit of the same quantity for a sequence of finite-dimensional normal matrices.

scholarly journals On sinc quadrature approximations of fractional powers of regularly accretive operators

2019 ◽  
Vol 27 (2) ◽  
pp. 57-68 ◽  
Author(s):  
Andrea Bonito ◽  
Wenyu Lei ◽  
Joseph E. Pasciak
Keyword(s):  
Finite Element ◽  
Numerical Experiments ◽  
Finite Element Approximation ◽  
Integral Approach ◽  
Element Approximation ◽  
Accretive Operators ◽  
Fractional Powers ◽  
Quadrature Scheme ◽  
Numer Anal ◽  
Sinc Quadrature

Abstract We consider the finite element approximation of fractional powers of regularly accretive operators via the Dunford–Taylor integral approach. We use a sinc quadrature scheme to approximate the Balakrishnan representation of the negative powers of the operator as well as its finite element approximation. We improve the exponentially convergent error estimates from [A. Bonito and J. E. Pasciak, IMA J. Numer. Anal., 37 (2016), No. 3, 1245–1273] by reducing the regularity required on the data. Numerical experiments illustrating the new theory are provided.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

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