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.

The real interpolation method on couples of intersections

2006 ◽  
Vol 40 (3) ◽  
pp. 218-221
Author(s):  
S. V. Astashkin ◽  
P. Sunehag
Keyword(s):  
Interpolation Method ◽  
Real Interpolation ◽  
The Real ◽  
Real Interpolation Method

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.

The Real Interpolation Method

1976 ◽  
pp. 38-86
Author(s):  
Jöran Bergh ◽  
Jörgen Löfström
Keyword(s):  
Interpolation Method ◽  
Real Interpolation ◽  
The Real ◽  
Real Interpolation Method

One property of functors of the real interpolation method

1985 ◽  
Vol 38 (3) ◽  
pp. 725-732
Author(s):  
S. V. Astashkin
Keyword(s):  
Interpolation Method ◽  
Real Interpolation ◽  
The Real ◽  
Real Interpolation Method

scholarly journals The problem of trigonometric Fourier series multipliers of classes in λp,q spaces

2020 ◽  
Vol 100 (4) ◽  
pp. 17-25
Author(s):  
A. Bakhyt ◽  
◽  
N.T. Tleukhanova ◽  
Keyword(s):  
Weighted Space ◽  
Interpolation Method ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Real Interpolation ◽  
Complex Interpolation ◽  
O’Neil Inequality ◽  
Real Interpolation Method ◽  
Necessary And Sufficient ◽  
Increasing Sequences

In this article, we consider weighted spaces of numerical sequences λp,q, which are defined as sets of sequences a = {ak}^∞_k=1, for which the norm ||a||λp,q :=\sum^∞_k=1|ak|^q k^(q/p −1)^1/q<∞ is finite. In the case of non-increasing sequences, the norm of the space λp,q coincides with the norm of the classical Lorentz space lp,q. Necessary and sufficient conditions are obtained for embeddings of the space λp,q into the space λp1,q1. The interpolation properties of these spaces with respect to the real interpolation method are studied. It is shown that the scale of spaces λp,q is closed in the relative real interpolation method, as well as in relative to the complex interpolation method. A description of the dual space to the weighted space λp,q is obtained. Specifically, it is shown that the space is reflective, where p', q' are conjugate to the parameters p and q. The paper also studies the properties of the convolution operator in these spaces. The main result of this work is an O’Neil type inequality. The resulting inequality generalizes the classical Young-O’Neil inequality. The research methods are based on the interpolation theorems proved in this paper for the spaces λp,q.

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