scholarly journals A truncated real interpolation method and characterizations of screened Sobolev spaces

2020 ◽  
Vol 19 (12) ◽  
pp. 5509-5566
Author(s):  
Noah Stevenson ◽  
◽  
Ian Tice
Keyword(s):  
Sobolev Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Real Interpolation Method

Real Interpolation of Sobolev Spaces on Subdomains of Rn

1978 ◽  
Vol 30 (01) ◽  
pp. 190-214 ◽  
Author(s):  
R. A. Adams ◽  
J. J. F. Fournier
Keyword(s):  
Sobolev Space ◽  
Fractional Order ◽  
Sobolev Spaces ◽  
Besov Spaces ◽  
Interpolation Method ◽  
A Priori ◽  
Real Interpolation ◽  
Convenient Tool ◽  
Real Interpolation Method ◽  
Nikolskii Spaces

The real interpolation method is a very convenient tool in the study of imbedding relationships among Sobolev spaces and some of their fractional order generalizations, (Besov spaces, Nikolskii spaces etc.) Central to the application of these methods is the a priori determination that a given Sobolev space Wk'p(Ω) belongs to an appropriate class of spaces intermediate between two other “extreme” 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:

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