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INTERPOLATION SPACES AND INTERPOLATION GROUPS
"... This is a temporary version of the notes which were used for the second part of my lecture of 30/9/2010. Hopefully a somewhat more definitive version will be available later. Some parts of the lecture do not appear in these notes, and of course we did not get to the latter part of these notes in the ..."
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This is a temporary version of the notes which were used for the second part of my lecture of 30/9/2010. Hopefully a somewhat more definitive version will be available later. Some parts of the lecture do not appear in these notes, and of course we did not get to the latter part of these notes in the lecture. 1. Compatible couples of quasinormed abelian groups. Definition 1. Let A be an abelian group where the group operation is denoted by + and the identity element by 0. A functional ‖· ‖ on A is said to be a quasinorm or a cquasinorm on A if it satisfies (i) ‖a ‖ ≥ 0 for all a ∈ A. (ii) ‖a ‖ = 0 if and only if a = 0. (iii) ‖−a ‖ = ‖a ‖ for all a ∈ A. (iv) There exists a positive constant c such that ‖a + b ‖ ≤ c (‖a ‖ + ‖b‖) for all a and b in A. A quasinormed abelian group is thus an abelian group equipped with a quasinorm. If c = 1 then the 1quasinorm ‖· ‖ is also referred to as a norm, and we have a normed abelian group. Theorem 2. Let A be a cquasinormed abelian group with cquasinorm denoted by ‖·‖A. Let ρ be the positive on A such that number which satisfies (2c) ρ = 2. Then there exists a 1quasinorm ‖· ‖ ∗ A (1.1) ‖a ‖ ∗
Nonlinear approximation and interpolation spaces
 J. APPROX. THEORY
, 2001
"... We study nterm wavelettype approximations in Besov and TriebelLizorkin spaces. In particular, we characterize spaces of functions which have prescribed degree of nterm approximation in terms of interpolation spaces. These results are applied to identify interpolation spaces between Triebel–Lizor ..."
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We study nterm wavelettype approximations in Besov and TriebelLizorkin spaces. In particular, we characterize spaces of functions which have prescribed degree of nterm approximation in terms of interpolation spaces. These results are applied to identify interpolation spaces between Triebel
IDENTIFICATION OF SOME REAL INTERPOLATION SPACES
, 2006
"... We interrelate the real interpolation spaces associated with the couples (X,Y), (X + Y, Y), (X,X ∩ Y), and (X + Y, X ∩ Y), proving among others the identities ..."
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We interrelate the real interpolation spaces associated with the couples (X,Y), (X + Y, Y), (X,X ∩ Y), and (X + Y, X ∩ Y), proving among others the identities
Optimal Interpolating Spaces Preserving Shape
, 1999
"... In this paper we study the existence and characterization of spaces which are images of minimalnorm projections that are required to interpolate at given functionals and satisfy additional shapepreserving requirements. We will call such spaces optimal interpolating spaces preserving shape. This in ..."
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In this paper we study the existence and characterization of spaces which are images of minimalnorm projections that are required to interpolate at given functionals and satisfy additional shapepreserving requirements. We will call such spaces optimal interpolating spaces preserving shape
View Interpolation for Image Synthesis
"... Imagespace simplifications have been used to accelerate the calculation of computer graphic images since the dawn of visual simulation. Texture mapping has been used to provide a means by which images may themselves be used as display primitives. The work reported by this paper endeavors to carry t ..."
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Cited by 603 (0 self)
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Imagespace simplifications have been used to accelerate the calculation of computer graphic images since the dawn of visual simulation. Texture mapping has been used to provide a means by which images may themselves be used as display primitives. The work reported by this paper endeavors to carry
A Short Introduction to Interpolation Spaces
, 2012
"... 1 Hilbert space interpolation Let V1 ⊂ V0 be two Hilbert spaces with dense embedding. For simplicity we assume that ..."
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1 Hilbert space interpolation Let V1 ⊂ V0 be two Hilbert spaces with dense embedding. For simplicity we assume that
Interpolation Spaces and Optimal Multilevel Preconditioners
 in Proceedings of the 7th International Conference on Domain Decomposition Methods
, 1994
"... . This paper throws light on the connection between the optimal condition number estimate for the BPX method and constructive approximation theory. We provide a machinery, which allows to understand the optimality as a consequence of an approximation property and an inverse inequality in H ..."
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Cited by 6 (2 self)
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. This paper throws light on the connection between the optimal condition number estimate for the BPX method and constructive approximation theory. We provide a machinery, which allows to understand the optimality as a consequence of an approximation property and an inverse inequality in H
On the Structure of Ultraproducts of Real Interpolation Spaces
"... DacunhaCastelle and Krivine introduced ultraproducts in Banach space theory, inspired in model theory of Logic, in [4] in 1972. Ultraproducts become a powerful tool in many applications (see for instance [6], [11], [8], [5] and [10]). One of the more important questions is to know the structure ..."
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DacunhaCastelle and Krivine introduced ultraproducts in Banach space theory, inspired in model theory of Logic, in [4] in 1972. Ultraproducts become a powerful tool in many applications (see for instance [6], [11], [8], [5] and [10]). One of the more important questions is to know the structure
Results 1  10
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294,773