The discussion clarifies the differences between H1 and H2 Hilbert spaces, which are specific Sobolev spaces denoted as H^k = W^{k,2}. The "2" indicates the use of the L^2 norm, while "k" signifies the inclusion of derivatives up to the kth order in the function analysis. Specifically, the norm is defined as ||f||^2_{H^k} = ||f||^2_{W^{k,2}} = ∑_{i=0}^k ∫ dt |f^{(i)}|^2, highlighting the importance of derivatives in these spaces.
PREREQUISITESMathematicians, physicists, and engineers interested in advanced functional analysis, particularly those working with Sobolev spaces and their applications in various fields such as partial differential equations and quantum mechanics.
These are two special Sobolev spaces, namelyamalmirando said:Can somebody tell me the difference between H1 & H2 hilbert spaces?