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Extensions of linear operators from hyperplanes of l ( n )

Marco Baronti, Vito Fragnelli, Grzegorz Lewicki (1995)

Commentationes Mathematicae Universitatis Carolinae

Let Y l ( n ) be a hyperplane and let A ( Y ) be given. Denote 𝒜 = { L ( l ( n ) , Y ) : L Y = A } and λ A = inf { L : L 𝒜 } . In this paper the problem of calculating of the constant λ A is studied. We present a complete characterization of those A ( Y ) for which λ A = A . Next we consider the case λ A > A . Finally some computer examples will be presented.

Generalized Kronrod Patterson type imbedded quadratures

Sylvan Elhay, Jaroslav Kautský (1992)

Applications of Mathematics

We present algorithms for the determination of polynomials orthogonal with respect to a positive weight function multiplied by a polynomial with simple roots inside the interval of integration. We apply these algorithms to search for and calculate all possible sequences of imbedded quadratures of maximal polynomials order of precision for the generalized Laguerre and Hermite weight functions.

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