The reproducing Kernel of the Sobolev space on an interval
Copyright policy )The reproducing Kernel of the Sobolev space on an interval
Let H n ( a , b ) H^n(a,b) be the one-dimensional Sobolev Hilbert space of order n n on the interval ( a , b ) (a,b) ( n = 1 , 2 , … n=1,2,\dots ). The explicit form of the reproducing kernel of H n ( a , b ) H^n(a,b) on finite interval was already known in the case for n = 1 , 2 , 3 n=1,2,3 . In this paper we obtain the explicit form of the reproducing kernel of H n ( a , b ) H^n(a,b) on any interval for general n n .
reproducing kernel, one-dimensional Sobolev Hilbert space, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
reproducing kernel, one-dimensional Sobolev Hilbert space, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
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