Interpolation spaces and interpolation methods

1965 ◽  
Vol 68 (1) ◽  
pp. 51-117 ◽  
Author(s):  
N. Aronszajn ◽  
E. Gagliardo
Keyword(s):  
Interpolation Spaces ◽  
Interpolation Methods

scholarly journals Some Reiteration Theorems for R , L , R R , R L , L R , and L L Limiting Interpolation Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Leo R. Ya. Doktorski
Keyword(s):  
Lorentz Spaces ◽  
Interpolation Spaces ◽  
Interpolation Methods

We consider the K -interpolation methods involving slowly varying functions. We establish some reiteration formulae including so-called L or R limiting interpolation spaces as well as the R R , R L , L R , and L L extremal interpolation spaces. These spaces arise in the limiting situations. The proofs of most reiteration formulae are based on Holmstedt-type formulae. Applications to grand and small Lorentz spaces in critical cases are given.

scholarly journals K-ENVELOPES FOR REAL INTERPOLATION METHODS

2012 ◽  
Vol 55 (2) ◽  
pp. 293-307
Author(s):  
MING FAN
Keyword(s):  
Function Space ◽  
Upper Bounds ◽  
Function Spaces ◽  
Real Interpolation ◽  
Rearrangement Invariant Space ◽  
Interpolation Spaces ◽  
Invariant Space ◽  
Bounded Operators ◽  
Fundamental Function ◽  
Interpolation Methods

AbstractIn this paper, we study the K-envelopes of the real interpolation methods with function space parameters in the sense of Brudnyi and Kruglyak [Y. A. Brudnyi and N. Ja. Kruglyak, Interpolation functors and interpolation spaces (North-Holland, Amsterdam, Netherlands, 1991)]. We estimate the upper bounds of the K-envelopes and the interpolation norms of bounded operators for the KΦ-methods in terms of the fundamental function of the rearrangement invariant space related to the function space parameter Φ. The results concerning the quasi-power parameters and the growth/continuity envelopes in function spaces are obtained.

Effects of Sampling and Interpolation Methods on Accuracy of Extracted Watershed Features

2021 ◽  
Vol 26 (3) ◽  
pp. 05020053
Author(s):  
Jingwei Hou ◽  
Meiyan Zheng ◽  
Moyan Zhu ◽  
Yanjuan Wang
Keyword(s):  
Interpolation Methods

scholarly journals Spatio-Temporal Analysis of Water Quality Parameters in Machángara River with Nonuniform Interpolation Methods

Water ◽  
2016 ◽  
Vol 8 (11) ◽  
pp. 507 ◽  
Author(s):  
Iván Vizcaíno ◽  
Enrique Carrera ◽  
Margarita Sanromán-Junquera ◽  
Sergio Muñoz-Romero ◽  
José Luis Rojo-Álvarez ◽  
...  
Keyword(s):  
Water Quality ◽  
Temporal Analysis ◽  
Quality Parameters ◽  
Water Quality Parameters ◽  
Interpolation Methods ◽  
Spatio Temporal

Interpolation methods for two-way coupled Euler-Lagrange simulation of finite-size bubbles

2021 ◽  
pp. 116566
Author(s):  
Xinghao Yang ◽  
Mark-Patrick Mühlhausen ◽  
Jochen Fröhlich
Keyword(s):  
Finite Size ◽  
Interpolation Methods

scholarly journals GIS-Based Approach to Spatio-Temporal Interpolation of Atmospheric CO2 Concentrations in Limited Monitoring Dataset

Atmosphere ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 384
Author(s):  
Yaroslav Bezyk ◽  
Izabela Sówka ◽  
Maciej Górka ◽  
Jan Blachowski
Keyword(s):  
Seasonal Variability ◽  
Sampling Strategy ◽  
Climate Impacts ◽  
Air Pollutant ◽  
Urban Atmosphere ◽  
Atmospheric Co2 ◽  
Spatial Characteristic ◽  
Interpolation Methods ◽  
Co2 Levels ◽  
The City

Understanding the magnitude and distribution of the mixes of the near-ground carbon dioxide (CO2) components spatially (related to the surface characteristics) and temporally (over seasonal timescales) is critical to evaluating present and future climate impacts. Thus, the application of in situ measurement approaches, combined with the spatial interpolation methods, will help to explore variations in source contribution to the total CO2 mixing ratios in the urban atmosphere. This study presents the spatial characteristic and temporal trend of atmospheric CO2 levels observed within the city of Wroclaw, Poland for the July 2017–August 2018 period. The seasonal variability of atmospheric CO2 around the city was directly measured at the selected sites using flask sampling with a Picarro G2201-I Cavity Ring-Down Spectroscopy (CRDS) technique. The current work aimed at determining the accuracy of the interpolation techniques and adjusting the interpolation parameters for estimating the magnitude of CO2 time series/seasonal variability in terms of limited observations during the vegetation and non-vegetation periods. The objective was to evaluate how different interpolation methods will affect the assessment of air pollutant levels in the urban environment and identify the optimal sampling strategy. The study discusses the schemes for optimization of the interpolation results that may be adopted in areas where no observations are available, which is based on the kriging error predictions for an appropriate spatial density of measurement locations. Finally, the interpolation results were extended regarding the average prediction bias by exploring additional experimental configurations and introducing the limitation of the future sampling strategy on the seasonal representation of the CO2 levels in the urban area.

Sign in / Sign up

Export Citation Format

Share Document