Projects per year
Abstract
We describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator. We show that, in this setting, spectral multipliers follow from resolvent or semigroup type estimates. The most notable point of the paper is that our approach is very flexible and can be applied even if the corresponding ambient space does not satisfy the doubling condition or if the semigroup generated by an operator is not uniformly bounded. As a corollary we obtain Lp spectrum independence for several second order differential operators and recover some known results. Our examples include the Laplace–Belltrami operator on manifolds with ends and Schrödinger operators with strongly subcritical potentials.
Original language | English |
---|---|
Pages (from-to) | 555-570 |
Number of pages | 16 |
Journal | Mathematische Zeitschrift |
Volume | 294 |
Issue number | 1-2 |
Early online date | 8 Apr 2019 |
DOIs | |
Publication status | Published - Feb 2020 |
Keywords
- Spectral multipliers
- Non-homogeneous type spaces
- Finite propagation speed property
- Lᴾ spectrum independence
- Manifolds with ends
- Schrödinger operators
Fingerprint
Dive into the research topics of 'Spectral multipliers via resolvent type estimates on non-homogeneous metric measure spaces'. Together they form a unique fingerprint.Projects
- 1 Active
-
Heat kernel and Riesz transform on non-compact metric measure spaces
Sikora, A. & Coulhon, T.
1/02/13 → …
Project: Research