On eigenfunction expansions of differential equations with degenerating weight

2020/07/03 by Mogilevskii, Vadim
#34B09 #34B40 #34L10 #47A06 #47A20 #47B25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2007.01782

Abstract

Let A be a symmetric operator. By using the method of boundary triplets we parameterize in terms of a Nevanlinna parameter τ all exit space extensions \wt A=\wt A^* of A with the discrete spectrum \s(\wt A) and characterize the Shtraus family of \wt A in terms of abstract boundary conditions. Next we apply these results to the eigenvalue problem for the 2r-th order differential equation l[y]= ł\D(x)y on an interval [a,b), -∞

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