scholarly journals Real and complex interpolation methods for finite and infinite families of Banach spaces

1987 ◽  
Vol 66 (3) ◽  
pp. 234-290 ◽  
Author(s):  
Michael Cwikel ◽  
Svante Janson
Keyword(s):  
Banach Spaces ◽  
Complex Interpolation ◽  
Interpolation Methods

Research about Influencing Factor on Interpolation Accuracy in Data Exchange of Fluid-Structure Interaction

2013 ◽  
Vol 318 ◽  
pp. 100-107
Author(s):  
Zhen Shen ◽  
Biao Wang ◽  
Hui Yang ◽  
Yun Zheng
Keyword(s):  
Data Exchange ◽  
Shape Function ◽  
Interpolation Method ◽  
Matching Condition ◽  
Optimal Interpolation ◽  
Complex Interpolation ◽  
Interpolation Function ◽  
Interpolation Methods ◽  
Interpolation Accuracy ◽  
Lower Accuracy

Six kinds of interpolation methods, including projection-shape function method, three-dimensional linear interpolation method, optimal interpolation method, constant volume transformation method and so on, were adoped in the study of interpolation accuracy. From the point of view about the characterization of matching condition of two different grids and interpolation function, the infuencing factor on the interpolation accuracy was studied. The results revealed that different interpolation methods had different interpolation accuracy. The projection-shape function interpolation method had the best effect and the more complex interpolation function had lower accuracy. In many cases, the matching condition of two grids had much greater impact on the interpolation accuracy than the method itself. The error of interpolation method is inevitable, but the error caused by the grid quality could be reduced through efforts.

scholarly journals ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION

2020 ◽  
pp. 1-32
Author(s):  
Jesús M. F. Castillo ◽  
Willian H. G. Corrêa ◽  
Valentin Ferenczi ◽  
Manuel González
Keyword(s):  
Unit Circle ◽  
Banach Spaces ◽  
Local Stability ◽  
Interpolation Method ◽  
Complex Interpolation ◽  
Analytic Family ◽  
Köthe Spaces ◽  
The Stability ◽  
Stability Results ◽  
Differential Process

We study the stability of the differential process of Rochberg and Weiss associated with an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of Köthe function spaces, we complete earlier results of Kalton (who showed that there is global bounded stability for pairs of Köthe spaces) by showing that there is global (bounded) stability for families of up to three Köthe spaces distributed in arcs on the unit circle while there is no (bounded) stability for families of four or more Köthe spaces. In the context of arbitrary pairs of Banach spaces, we present some local stability results and some global isometric stability results.

Complex interpolation for families of Banach spaces

1979 ◽  
pp. 269-282 ◽  
Author(s):  
R. Coifman ◽  
M. Cwikel ◽  
R. Rochberg ◽  
Y. Sagher ◽  
G. Weiss
Keyword(s):  
Banach Spaces ◽  
Complex Interpolation

scholarly journals A theory of complex interpolation for families of Banach spaces

1982 ◽  
Vol 43 (3) ◽  
pp. 203-229 ◽  
Author(s):  
R.R Coifman ◽  
M Cwikel ◽  
R Rochberg ◽  
Y Sagher ◽  
G Weiss
Keyword(s):  
Banach Spaces ◽  
Complex Interpolation

Interpolation of Morrey Spaces on Metric Measure Spaces

2014 ◽  
Vol 57 (3) ◽  
pp. 598-608 ◽  
Author(s):  
Yufeng Lu ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Interpolation Method ◽  
Interpolation Theorem ◽  
Morrey Spaces ◽  
Complex Interpolation ◽  
Metric Measure Spaces ◽  
Interpolation Methods ◽  
Measure Spaces

AbstractIn this article, via the classical complex interpolation method and some interpolation methods traced to Gagliardo, the authors obtain an interpolation theorem for Morrey spaces on quasimetric measure spaces, which generalizes some known results on ℝn.

Complex interpolation for family of Banach spaces

1982 ◽  
Vol 34 (1) ◽  
pp. 26-36 ◽  
Author(s):  
S. G. Krein ◽  
L. I. Nikolova
Keyword(s):  
Banach Spaces ◽  
Complex Interpolation

scholarly journals On the connection between real and complex interpolation of quasi-banach spaces

1998 ◽  
Vol 122 (1) ◽  
pp. 17-37 ◽  
Author(s):  
Fernando Cobos ◽  
Jaak Peetre ◽  
Lars Erik Persson
Keyword(s):  
Banach Spaces ◽  
Complex Interpolation

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.

scholarly journals Interpolation theorem for Nikol’skii-Besov type spaceswith mixed metric

2020 ◽  
Vol 100 (4) ◽  
pp. 33-42
Author(s):  
K.A. Bekmaganbetov ◽  
◽  
K.Ye. Kervenev ◽  
Ye. Toleugazy ◽  
◽  
...  
Keyword(s):  
Besov Space ◽  
Besov Spaces ◽  
Interpolation Theorem ◽  
Discrete Space ◽  
Mixed Derivative ◽  
Complex Interpolation ◽  
Interpolation Methods ◽  
Mixed Metric ◽  
Vector Valued

In this paper we study the interpolation properties of Nikol’skii-Besov spaces with a dominant mixed derivative and mixed metric with respect to anisotropic and complex interpolation methods. An interpolation theorem is proved for a weighted discrete space of vector-valued sequences l^α_q(A). It is shown that the Nikol’skii-Besov space under study is a retract of the space l^α_q(Lp). Based on the above results, interpolation theorems were obtained for Nikol’skii-Besov spaces with the dominant mixed derivative and mixed metric.

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