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Full-Text Articles in Other Mathematics
The Fock Space As A De Branges–Rovnyak Space, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
The Fock Space As A De Branges–Rovnyak Space, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that de Branges–Rovnyak spaces include as special cases a number of spaces, such as the Hardy space, the Fock space, the Hardy–Sobolev space and the Dirichlet space. We present a general framework in which all these spaces can be obtained by specializing a sequence that appears in the construction. We show how to exploit this approach to solve interpolation problems in the Fock space.
About A Non-Standard Interpolation Problem, Daniel Alpay, Alain Yger
About A Non-Standard Interpolation Problem, Daniel Alpay, Alain Yger
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein algebra, using the Lagrange interpolation polynomial, plays a key role in the arguments.
Interpolation By Polynomials With Symmetries, Daniel Alpay, Izchak Lewkowicz
Interpolation By Polynomials With Symmetries, Daniel Alpay, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
We here specialize the standard matrix-valued polynomial interpolation to the case where on the imaginary axis the interpolating polynomials admit various symmetries: Positive semidefinite, Skew-Hermitian, J- Hermitian, Hamiltonian and others.
The procedure is comprized of three stages, illustrated through the case where on $i\R$ the interpolating polynomials are to be positive semidefinite. We first, on the expense of doubling the degree, obtain a minimal degree interpolating polynomial P(s) which on $i\R$ is Hermitian. Then we find all polynomials Ψ(s), vanishing at the interpolation points which are positive semidefinite on $i\R$. Finally, using the fact that the set of positive semidefinite …