Stone´s Theorem and Applications
(2010) In Bachelor's Theses in Mathematical Sciences MATX01 20101Mathematics (Faculty of Sciences)
- Abstract
- Stone's theorem establishes a bijection between self-adjoint operators on a Hilbert space and one-parameter groups of strongly continuous, unitary operators via a functional calculus. We will rst introduce the necessary terminology and then prove this result. We will study many of the numerous applications of Stone's theorem, especially those in quantum mechanics. We will also consider non-physics-related applications including an elegant proof of Bochner's theorem on positive-denite functions.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/2439974
- author
- Möller, Sven
- supervisor
- organization
- course
- MATX01 20101
- year
- 2010
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFMA-4005-2010
- ISSN
- 1654-6229
- other publication id
- 2010:K2
- language
- English
- id
- 2439974
- date added to LUP
- 2014-12-15 14:43:42
- date last changed
- 2018-10-11 16:22:41
@misc{2439974, abstract = {{Stone's theorem establishes a bijection between self-adjoint operators on a Hilbert space and one-parameter groups of strongly continuous, unitary operators via a functional calculus. We will rst introduce the necessary terminology and then prove this result. We will study many of the numerous applications of Stone's theorem, especially those in quantum mechanics. We will also consider non-physics-related applications including an elegant proof of Bochner's theorem on positive-denite functions.}}, author = {{Möller, Sven}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Stone´s Theorem and Applications}}, year = {{2010}}, }