The Spectrum of a Composition Operator and Calderón’s Complex Interpolation

2010 ◽  
pp. 451-467 ◽  
Author(s):  
Matthew A. Pons
Keyword(s):  
Composition Operator ◽  
Complex Interpolation

Continuity of the Norm of a Composition Operator

2003 ◽  
Vol 45 (3) ◽  
pp. 351-358 ◽  
Author(s):  
David B. Pokorny ◽  
Jonathan E. Shapiro
Keyword(s):  
Composition Operator

Fractional abstract Cauchy problem on complex interpolation scales

2020 ◽  
Vol 23 (4) ◽  
pp. 1125-1140
Author(s):  
Andriy Lopushansky ◽  
Oleh Lopushansky ◽  
Anna Szpila
Keyword(s):  
Cauchy Problem ◽  
Time Derivative ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Sectorial Operator ◽  
Complex Interpolation ◽  
Bounded Domains ◽  
Initial Boundary Value Problems ◽  
Fractional Time Derivative ◽  
Initial Boundary Value

AbstractAn fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

scholarly journals EXPLICIT INTERPOLATION BOUNDS BETWEEN HARDY SPACE AND

2013 ◽  
Vol 95 (2) ◽  
pp. 158-168
Author(s):  
H.-Q. BUI ◽  
R. S. LAUGESEN
Keyword(s):  
Growth Rate ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Bounded Mean Oscillation ◽  
Complex Interpolation ◽  
Bounded Linear ◽  
Exponential Bound ◽  
Mean Oscillation ◽  
Good Lambda Inequality ◽  
Interpolation Result

AbstractEvery bounded linear operator that maps ${H}^{1} $ to ${L}^{1} $ and ${L}^{2} $ to ${L}^{2} $ is bounded from ${L}^{p} $ to ${L}^{p} $ for each $p\in (1, 2)$, by a famous interpolation result of Fefferman and Stein. We prove ${L}^{p} $-norm bounds that grow like $O(1/ (p- 1))$ as $p\downarrow 1$. This growth rate is optimal, and improves significantly on the previously known exponential bound $O({2}^{1/ (p- 1)} )$. For $p\in (2, \infty )$, we prove explicit ${L}^{p} $ estimates on each bounded linear operator mapping ${L}^{\infty } $ to bounded mean oscillation ($\mathit{BMO}$) and ${L}^{2} $ to ${L}^{2} $. This $\mathit{BMO}$ interpolation result implies the ${H}^{1} $ result above, by duality. In addition, we obtain stronger results by working with dyadic ${H}^{1} $ and dyadic $\mathit{BMO}$. The proofs proceed by complex interpolation, after we develop an optimal dyadic ‘good lambda’ inequality for the dyadic $\sharp $-maximal operator.

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 A Note on Unbounded Hyponormal Composition Operators inL2-Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Piotr Budzyński
Keyword(s):  
Composition Operator ◽  
Composition Operators

We construct an unbounded hyponormal composition operatorCϕinL2-space such that the domains ofCϕ2andCϕ2are trivial.

scholarly journals Complex Interpolation with Derivatives of Analytic Functions

1994 ◽  
Vol 120 (2) ◽  
pp. 380-402 ◽  
Author(s):  
M. Fan ◽  
S. Kaijser
Keyword(s):  
Analytic Functions ◽  
Complex Interpolation ◽  
Derivatives Of

scholarly journals Complex interpolation and twisted twisted Hilbert spaces

2015 ◽  
Vol 276 (2) ◽  
pp. 287-307 ◽  
Author(s):  
Félix Cabello Sánchez ◽  
Jesús Castillo ◽  
Nigel Kalton
Keyword(s):  
Hilbert Spaces ◽  
Complex Interpolation

scholarly journals Bloch-Type Spaces of Minimal Surfaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Guanghua He ◽  
Xi Fu ◽  
Hancan Zhu
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Minimal Surfaces ◽  
Lipschitz Functions ◽  
Type Spaces

We study Bloch-type spaces of minimal surfaces from the unit disk D into Rn and characterize them in terms of weighted Lipschitz functions. In addition, the boundedness of a composition operator Cϕ acting between two Bloch-type spaces is discussed.

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