Search results for "Hermite function"
showing 3 items of 3 documents
Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces
2017
We consider quasi-Banach spaces that lie between a Gelfand–Shilov space, or more generally, Pilipovi´c space, \(\mathcal{H}\), and its dual, \(\mathcal{H}^\prime\) . We prove that for such quasi-Banach space \(\mathcal{B}\), there are convenient Hilbert spaces, \(\mathcal{H}_{k}, k=1,2\), with normalized Hermite functions as orthonormal bases and such that \(\mathcal{B}\) lies between \(\mathcal{H}_1\; \mathrm{and}\;\mathcal{H}_2\), and the latter spaces lie between \(\mathcal{H}\; \mathrm{and}\;\mathcal{H}^\prime\).
Numerical Solution of Foodstuff Freezing Problems Using Radial Basis Functions
2013
This work presents a novel numerical approach for the solution of time dependent non-linear freezing processes in terms of radial basis function Hermite approach. The proposed scheme is applied to a mashed potato sample during its freezing; evaluation of time evolution of the temperature profile at the core of the sample is carried out. Food thermal properties are highly dependent on temperature and the mathematical problem becomes highly non-linear and therefore particularly difficult to solve. Incorporating a Kirchhoff transformation significantly reduces the non-linearity. The robustness of the scheme is tested by comparison with experimental results available in literature.
Mapping properties for the Bargmann transform on modulation spaces
2010
We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.