Hilbert spaces and functional analysis
Espacios de Hilbert y análisis funcional
- Date
- 1906-1912 · confidence high
- Place
- Göttingen, Germany
- Credited to
- David Hilbert (integral equations), Erhard Schmidt, Frigyes Riesz; axiomatisation by John von Neumann (1929)
- People
- 👤 David Hilbert1862–1943👤 Erhard Schmidt1876–1959👤 Frigyes Riesz1880–1956
- Field
- Knowledge & symbols
What was discovered
Infinite-dimensional spaces with an inner product in which functions are treated as vectors and operators as infinite matrices, with spectral theory. It is the mathematical framework of quantum mechanics.
Banach generalised the theory to complete normed spaces in Lwów (1922-1932).
What it led to
- quantum mechanics
- functional analysis
- operator theory
- signal processing
Built on
- Fourier series and transform1807
- Measure theory and Lebesgue integral1902
- Fourier series
- Fredholm integral equations