On interpolation of strictly (co-)singular linear operators

1989 ◽  
Vol 112 (3-4) ◽  
pp. 263-269 ◽  
Author(s):  
O. J. Beucher
Keyword(s):  
Banach Spaces ◽  
Interpolation Method ◽  
Interpolation Property ◽  
Linear Operators ◽  
Real Interpolation ◽  
Injective Hull ◽  
The Real ◽  
Real Interpolation Method ◽  
Strictly Singular ◽  
The Ideal

SynopsisWe show that the property of linear operators to be in the surjective hull (injective hull) of the ideal of strictly singular (strictly cosingular) operators between Banach spaces is an interpolation property with respect to the real interpolation method with parameters 0 < ủ < 1 and < p < ℞.

scholarly journals A Maximal Description for the Real Interpolation Method in the Quasi-Banach Case.

2000 ◽  
Vol 87 (1) ◽  
pp. 22 ◽  
Author(s):  
Jöran Bergh ◽  
Fernando Cobos
Keyword(s):  
Banach Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
The Real ◽  
Real Method ◽  
Real Interpolation Method

We give a maximal description in the sense of Aronszajn-Gagliardo for the real method in the category of quasi-Banach spaces.

Real Interpolation with Logarithmic Functors and Reiteration

2000 ◽  
Vol 52 (5) ◽  
pp. 920-960 ◽  
Author(s):  
W. D. Evans ◽  
B. Opic
Keyword(s):  
Banach Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Real Interpolation Method ◽  
Original Scale ◽  
Limiting Values

AbstractWe present “reiteration theorems” with limiting values θ = 0 and θ = 1 for a real interpolation method involving broken-logarithmic functors. The resulting spaces lie outside of the original scale of spaces and to describe them new interpolation functors are introduced. For an ordered couple of (quasi-) Banach spaces similar results were presented without proofs by Doktorskii in [D].

Synthesis of Control System for an Unstable Object by Real Interpolation Method

2014 ◽  
Vol 905 ◽  
pp. 439-442
Author(s):  
A.V. Voronin ◽  
Valeriy Ivanovich Goncharov ◽  
Tatyana A. Shchelkanova
Keyword(s):  
Control System ◽  
Automatic Control ◽  
Automatic Control System ◽  
Wide Class ◽  
Reference Model ◽  
Interpolation Method ◽  
Real Interpolation ◽  
The Real ◽  
Real Interpolation Method

The article deals with the problem of the synthesis of control system for unstable object. The novelty of the approach has two main elements. Firstly, there is achieved the generalization of the real interpolation method of the synthesis of a wide class of objects, which includes unstable objects. Secondly, the approach allows eliminating the step of factorization of corresponding polynomials. This step is required for the formation of the reference model of automatic control system for unstable object.

Hardware Implementation Tasks to Configure Regulators

2014 ◽  
Vol 945-949 ◽  
pp. 2611-2616 ◽  
Author(s):  
Valery Goncharov ◽  
Ilya O. Ilyin ◽  
Andrey Kudryavtsev
Keyword(s):  
Mobile Device ◽  
Hardware Implementation ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Mathematical Software ◽  
The Real ◽  
Advantages And Disadvantages ◽  
Software Packages ◽  
Real Interpolation Method ◽  
Selection Of

The authors consider the problem of configuring regulators. This paper describes the selection of instrumental tools to create a mobile device, based on the real interpolation method, enabling to configure regulators without the use of mathematical software packages like Matlab or Mathcad. Also described are advantages and disadvantages of selecting hardware and software part for the mobile devise:

scholarly journals Reiteration Formulae for the Real Interpolation Method Including L or R Limiting Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Leo R. Ya. Doktorski
Keyword(s):  
Interpolation Method ◽  
Lorentz Spaces ◽  
Real Interpolation ◽  
Interpolation Spaces ◽  
The Real ◽  
Real Interpolation Method

We consider a real interpolation method defined by means of slowly varying functions. We present some reiteration formulae including so-called L or R limiting interpolation spaces. These spaces arise naturally in reiteration formulae for the limiting cases θ = 0 or θ = 1 . Applications to grand and small Lorentz spaces are given.

scholarly journals Stein interpolation for the real interpolation method

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Nick Lindemulder ◽  
Emiel Lorist
Keyword(s):  
Interpolation Method ◽  
Real Interpolation ◽  
Complex Interpolation ◽  
The Real ◽  
Interpolation Methods ◽  
Complex Formulation ◽  
Closed Operators ◽  
Real Interpolation Method

AbstractWe prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real interpolation method. We apply this theorem to interpolate weighted $$L^p$$ L p -spaces and the sectoriality of closed operators with the real interpolation method.

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