Taking Limits Under the Integral Sign

Cunningham, Floyd F.

doi:10.1080/0025570x.1967.11975791

Cited by 5 publications

(2 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where we have taken the limit under the integral sign by virtue of the dominated convergence theorem 15 (see Appendix B). The asymptotic behavior of F…”

Section: B the Case ǫ = 2n +mentioning

confidence: 99%

The step-harmonic potential

Rizzi¹,

Piattella²,

Cacciatori³

et al. 2010

American Journal of Physics

View full text Add to dashboard Cite

International audienceWe analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to classify the independent solutions as equivalence classes of homotopic paths in the complex plane. We then consider the propagation of a wave packet reflected by the harmonic barrier and obtain an expression for the interaction time as a function of the peak energy. For high energies we recover the classical half-period limit

show abstract

“…where we have taken the limit under the integral sign by virtue of the dominated convergence theorem 15 (see Appendix B). The asymptotic behavior of F…”

Section: B the Case ǫ = 2n +mentioning

confidence: 99%

The step-harmonic potential

Rizzi¹,

Piattella²,

Cacciatori³

et al. 2010

American Journal of Physics

View full text Add to dashboard Cite

show abstract

“…Finally, each f n (for is non‐negative, and bounded above by the function: and h , being clearly continuous on [ T , T ″], is also Riemann integrable on [ T , T ″]. Thus, we can conclude that: See Cunningham (1967, theorem 2, p. 184) for the precise result that is being used.…”

mentioning

confidence: 92%

On competitive equitable paths under exhaustible resource constraints: The case of a growing population

Mitra

2008

Int J of Economic Theory

View full text Add to dashboard Cite

The paper examines the nature of competitive paths in an exhaustible resource model, which allows for a growing population. For competitive paths that are equitable in the sense that the per capita consumption level is constant over time, the implicit investment rule is derived. This is seen to be a generalization of Hartwick's rule, obtained in the case of a stationary population. It is also shown that the existence of a competitive equitable path implies that a population can experience at most quasi‐arithmetic growth.

show abstract