EuDML | Browse

Page 1

Displaying 1 – 3 of 3

Complex interpolation for $2^{N}$ Banach spaces

Giovanni Dore, Davide Guidetti, Alberto Venni (1986)

Rendiconti del Seminario Matematico della Università di Padova

Computing discrete convolutions with verified accuracy via Banach algebras and the FFT

Jean-Philippe Lessard (2018)

Applications of Mathematics

We introduce a method to compute rigorous component-wise enclosures of discrete convolutions using the fast Fourier transform, the properties of Banach algebras, and interval arithmetic. The purpose of this new approach is to improve the implementation and the applicability of computer-assisted proofs performed in weighed $ℓ^{1}$ Banach algebras of Fourier/Chebyshev sequences, whose norms are known to be numerically unstable. We introduce some application examples, in particular a rigorous aposteriori...

Convergence of series of dilated functions and spectral norms of GCD matrices

Christoph Aistleitner, István Berkes, Kristian Seip, Michel Weber (2015)

Acta Arithmetica

We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are $(j^{- α})$ for some α ∈ (1/2,1), and the spectral norms of certain greatest common divisor (GCD) matrices. Utilizing recent bounds for these spectral norms, we obtain sharp conditions for the convergence in L² and for the almost everywhere convergence of series of dilated functions.

Displaying 1 – 3 of 3

Complex interpolation for 2 N Banach spaces

Computing discrete convolutions with verified accuracy via Banach algebras and the FFT

Convergence of series of dilated functions and spectral norms of GCD matrices

Currently displaying 1 – 3 of 3

Complex interpolation for $2^{N}$ Banach spaces