7.4. Spectral decompositions and the carleson condition

1984 ◽  
Vol 26 (5) ◽  
pp. 2152-2153
Author(s):  
V. I. Vasyunin ◽  
N. K. Nikol'skii ◽  
B. S. Pavlov
Keyword(s):  
Spectral Decompositions ◽  
Carleson Condition

SPECTRAL DECOMPOSITION OF R-MATRICES FOR EXCEPTIONAL LIE ALGEBRAS

1991 ◽  
Vol 06 (10) ◽  
pp. 923-927 ◽  
Author(s):  
S.M. SERGEEV
Keyword(s):  
Lie Algebras ◽  
Spectral Decomposition ◽  
Spectral Decompositions ◽  
Exceptional Lie Algebras ◽  
Exceptional Algebras ◽  
Vector Representations

In this paper spectral decompositions of R-matrices for vector representations of exceptional algebras are found.

Spectral Decomposition of the Elasticity Tensor

1992 ◽  
Vol 59 (4) ◽  
pp. 762-773 ◽  
Author(s):  
S. Sutcliffe
Keyword(s):  
Spectral Decomposition ◽  
Dimensional Space ◽  
Anisotropic Elasticity ◽  
Elasticity Tensor ◽  
Symmetry Groups ◽  
Stored Energy ◽  
Equilibrium Equations ◽  
Classical Symmetry ◽  
Spectral Decompositions ◽  
Acoustic Tensor

The elasticity tensor in anisotropic elasticity can be regarded as a symmetric linear transformation on the nine-dimensional space of second-order tensors. This allows the elasticity tensor to be expressed in terms of its spectral decomposition. The structures of the spectral decompositions are determined by the sets of invariant subspaces that are consistent with material symmetry. Eigenvalues always depend on the values of the elastic constants, but the eigenvectors are, in part, independent of these values. The structures of the spectral decompositions are presented for the classical symmetry groups of crystallography, and numerical results are presented for representative materials in each group. Spectral forms for the equilibrium equations, the acoustic tensor, and the stored energy function are also derived.

scholarly journals Fast calculation of modal interaction in large power systems using spectral decompositions of Gramians

2018 ◽  
Vol 51 (28) ◽  
pp. 564-569
Author(s):  
Alexey B. Iskakov ◽  
Alexandr V. Lavrikov ◽  
Igor B. Yadykin
Keyword(s):  
Power Systems ◽  
Modal Interaction ◽  
Large Power ◽  
Fast Calculation ◽  
Spectral Decompositions

ORTHONORMAL MRA WAVELETS: SPECTRAL FORMULAS AND ALGORITHMS

2012 ◽  
Vol 10 (01) ◽  
pp. 1250008 ◽  
Author(s):  
F. GÓMEZ-CUBILLO ◽  
Z. SUCHANECKI ◽  
S. VILLULLAS
Keyword(s):  
Multiresolution Analysis ◽  
Matrix Representation ◽  
Infinite Product ◽  
Scaling Functions ◽  
Compactly Supported ◽  
Orthonormal Bases ◽  
Spectral Decompositions ◽  
Product Matrix ◽  
Orthonormal Wavelets

Spectral decompositions of translation and dilation operators are built in terms of suitable orthonormal bases of L2(ℝ), leading to spectral formulas for scaling functions and orthonormal wavelets associated with multiresolution analysis (MRA). The spectral formulas are useful to compute compactly supported scaling functions and wavelets. It is illustrated with a particular choice of the orthonormal bases, the so-called Haar bases, which yield a new algorithm related to the infinite product matrix representation of Daubechies and Lagarias.

scholarly journals Three-Way Spectral Decompositions of High-Performance Military Aircraft Noise

AIAA Journal ◽  
2019 ◽  
Vol 57 (8) ◽  
pp. 3467-3479 ◽  
Author(s):  
Tracianne B. Neilsen ◽  
Aaron B. Vaughn ◽  
Kent L. Gee ◽  
S. Hales Swift ◽  
Alan T. Wall ◽  
...  
Keyword(s):  
High Performance ◽  
Aircraft Noise ◽  
Military Aircraft ◽  
Spectral Decompositions
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