Bochner's theorem
- Category
- STANDARD MATHEMATICS
- Definition
- A theorem characterising continuous positive-definite functions as Fourier transforms of non-negative measures.
- Math Level
- SPECIALIST
- Index Excerpt
- Bochner criterion
Bochner's theorem
Bochner's theorem characterises continuous positive-definite functions on Euclidean space as Fourier transforms of finite non-negative measures.
It provides a fundamental bridge between positive definiteness in the original domain and non-negative spectral structure in the frequency domain.
See also: positive definiteness, Fourier transform, spectral measure. .