Abstract
An approximation theory for families of quadratic forms is given. We show that if continuity conditions for a family of quadratic forms hold uniformly on an index set for the family, generalized signature approximation results hold. We then apply these results to randomized spline type Sturm-Liouville problems and obtain continuity of thenth eigenvalue for generalized Sturm-Liouville problems under weak hypotheses.
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Gregory, J., Hughes, H.R. A generalized approximation theory for quadratic forms: Application to randomized spline type Sturm-Liouville problems. J Theor Probab 8, 703–715 (1995). https://doi.org/10.1007/BF02218052
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DOI: https://doi.org/10.1007/BF02218052