On the eigenvalues of an integral equation arising in the theory of band-limited signals

Fuchs, Wolfgang

doi:10.1016/0022-247x(64)90017-4

Cited by 83 publications

(59 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As one can note, it has the same form of the derivative of the boundary datum and hence it vanishes for long times. In Figure 14 we present a section of the solution u(x, y, t) of the problem (23)- (25), in the same point x = 1 2 , for t ∈[0, 10]: as one can observe, the wave travelling away from the boundary assumes the same structure of the Dirichlet boundary datum but with diminishing intensity. Figure 15 shows the time-dependent behavior of the solution u(x, t) outside .…”

Section: Numerical Resultsmentioning

confidence: 97%

See 1 more Smart Citation

An energy approach to space–time Galerkin BEM for wave propagation problems

Aimi

Diligenti

Guardasoni

et al. 2009

Numerical Meth Engineering

View full text Add to dashboard Cite

International audienceIn this paper we consider Dirichlet or Neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential. Starting from a natural energy identity, a space–time weak formulation for 1D integral problems is briefly introduced, and continuity and coerciveness properties of the related bilinear form are proved. Then, a theoretical analysis of an extension of the introduced formulation for 2D problems is proposed, pointing out the novelty with respect to existing literature results. At last, various numerical simulations will be presented and discussed, showing unconditional stability of the space–time Galerkin boundary element method applied to the energetic weak problem

show abstract

Section: Numerical Resultsmentioning

confidence: 97%

“…As we have seen for 1D problems, we can consider the single-layer representation of the solution of (23)- (25):…”

Section: Dirichlet Problem and Its Energetic Weak Formulationmentioning

confidence: 99%

An energy approach to space–time Galerkin BEM for wave propagation problems

Aimi

Diligenti

Guardasoni

et al. 2009

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…We now state a lemma which is the basis of a trick used by Fuchs [11] in his derivation of the asymptotics of the eigenvalues of the sine kernel.…”

Section: Lemma 2 For Each I We Havementioning

confidence: 99%

Level-spacing distributions and the Airy kernel

Tracy¹,

Widom²

1993

Physics Letters B

787

1,168

View full text Add to dashboard Cite

“…To simplify the notation, we do not point it out. The above theorem was proved in [8], [22]; see also [2], [3], [9], [11], [12], [13], [14], [15], [16], [17], [20], [21] for a more complete treatment.…”

Section: Prolate Spheroidal Wavefunctionsmentioning

confidence: 99%

Recovering signals from inner products involving prolate spheroidals in the presence of jitter

Dabrowska

2004

Math. Comp.

View full text Add to dashboard Cite

Abstract. The paper deals with recovering band-and energy-limited signals from a finite set of perturbed inner products involving the prolate spheroidal wavefunctions. The measurement noise (bounded by δ) and jitter meant as perturbation of the ends of the integration interval (bounded by γ) are considered. The upper and lower bounds on the radius of information are established. We show how the error of the best algorithms depends on γ and δ. We prove that jitter causes error of order Ω 3 2 γ, where [−Ω, Ω] is a bandwidth, which is similar to the error caused by jitter in the case of recovering signals from samples.

show abstract

On the eigenvalues of an integral equation arising in the theory of band-limited signals

Cited by 83 publications

References 2 publications

An energy approach to space–time Galerkin BEM for wave propagation problems

An energy approach to space–time Galerkin BEM for wave propagation problems

Level-spacing distributions and the Airy kernel

Recovering signals from inner products involving prolate spheroidals in the presence of jitter

Contact Info

Product

Resources

About