Tridiagonal Reproducing Kernels and Subnormality

We consider analytic reproducing kernel Hilbert spaces H with orthonormal bases of the form {(a(n) + b(n)z)z(n) : n >= 0}. If b(n) = 0 for all n, then H is a diagonal space and multiplication by z, M-z, is a weighted shift. Our focus is on providing extensive classes of examples for which M-z is a bounded subnormal operator on a tridiagonal space H where b(n) not equal 0. The Aronszajn sum of H and (1 - z)H where H is either the Hardy space or the Bergman space on the disk are two such examples.

A factor-analytic reinterpretation of the Clark-Trow "educational philosophies"

Each of four principal components analyses (n = 3,944) incorporated student self-ratings (Most accurate to Least accurate) on one of the four Clark-Trow educational philosophies: Vocational, Academic, Collegiate, Nonconformist. The analyses of these 25-variable correlation matrices yielded 2 factors differentially associated with educational philosophy: Sociability versus Independence (replacing Clark-Trow's "Identification with the College") and Liberalism versus Conservatism (replacing Clark-Trow's "Involvement with Ideas"). The Vocational philosophy was associated primarily with Conservatism, the Collegiate with Sociability, and the Nonconformist with Liberalism; the Academic was moderately associated with both Independence and Liberalism.