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Ridgelets and the Representation of Mutilated Sobolev Functions
Sobolev spaces Fourier transform singularities ridgelets orthonormal ridgelets nonlinear approximation sparsity
2015/6/17
We show that ridgelets, a system introduced in [4], are optimal to represent smooth multivariate functions that may exhibit linear singularities. For instance, let {u · x − b > 0} be an arbitrar...
Four-vector vs. four-scalar representation of the Dirac wave function
Four-vector four-scalar representation Dirac wave function
2011/3/2
In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar´e group.
The twisting representation of the $L$-function of a curve
twisting representation $L$-function of a curve
2011/2/21
Let C be a smooth projective curve defined over a number field k and let C′ be a twist of C. For every isomorphism : C′! C defined over a finite Galois extension L/k, we introduce a rational Artin re...
A Representation Theorem for Seneta Sequences
Regularly varying functions and sequence Seneta functions and sequences Representation theorem
2007/12/12
In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class $SO_c$.