Quasicontraction semigroup

Quasicontraction semigroup

In mathematical analysis, a C0-semigroup Γ(t), t ≥ 0, is called a quasicontraction semigroup if there is a constant ω such that ||Γ(t)|| ≤ exp(ωt) for all t ≥ 0. Γ(t) is called a contraction semigroup if ||Γ(t)|| ≤ 1 for all t ≥ 0.

See also

  • Hille-Yosida theorem

References

  • Renardy, Michael; Rogers, Robert C. (2004). An introduction to partial differential equations. Texts in Applied Mathematics 13 (Second edition ed.). New York: Springer-Verlag. p. xiv+434. ISBN 0-387-00444-0.  MR2028503