We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna... more We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna functions. The Schur transformation is defined for these classes of functions in several situations, and it is used to solve corresponding basic interpolation problems and problems of factorization of rational J-unitary matrix functions into elementary factors. A key role is played by the theory of reproducing kernel Pontryagin spaces and linear relations in these spaces.
We consider a scalar Nevanlinna-Pick interpolation problem with at most countably many interpolat... more We consider a scalar Nevanlinna-Pick interpolation problem with at most countably many interpolation points which lie in ℂ+∪ ℝ. Questions about the existence and uniqueness of the solutions are considered. In the case of nonuniqueness a description of all solutions is ...
We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna... more We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna functions. The Schur transformation is defined for these classes of functions in several situations, and it is used to solve corresponding basic interpolation problems and problems of factorization of rational J-unitary matrix functions into elementary factors. A key role is played by the theory of reproducing kernel Pontryagin spaces and linear relations in these spaces.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1984
Synopsis For a symmetric linear relation S with a directing mapping, the notion of a spectral fun... more Synopsis For a symmetric linear relation S with a directing mapping, the notion of a spectral function is defined by means of a BesselParseval inequality, and a description of all such spectral functions is given. As an application, we describe the set of all spectral functions ...
... 250 Math. Nachr. 162 (1993) Remark 2. In the situation of Remark 1, if 8 is a regular unitary... more ... 250 Math. Nachr. 162 (1993) Remark 2. In the situation of Remark 1, if 8 is a regular unitary dilation of T (see [AI], V.3), then llYT = 01.9,. and T'1.9,. = 0'1%. Indeed, if x E YT we have [x, x] = [Tx, Tx] = [POX, POX] I [Ox, Ox] [x, XI, hence Tx=Pox=oxandx=T+Zk=T+ox. Proposition 1.5. ...
We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna... more We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna functions. The Schur transformation is defined for these classes of functions in several situations, and it is used to solve corresponding basic interpolation problems and problems of factorization of rational J-unitary matrix functions into elementary factors. A key role is played by the theory of reproducing kernel Pontryagin spaces and linear relations in these spaces.
We consider a scalar Nevanlinna-Pick interpolation problem with at most countably many interpolat... more We consider a scalar Nevanlinna-Pick interpolation problem with at most countably many interpolation points which lie in ℂ+∪ ℝ. Questions about the existence and uniqueness of the solutions are considered. In the case of nonuniqueness a description of all solutions is ...
We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna... more We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna functions. The Schur transformation is defined for these classes of functions in several situations, and it is used to solve corresponding basic interpolation problems and problems of factorization of rational J-unitary matrix functions into elementary factors. A key role is played by the theory of reproducing kernel Pontryagin spaces and linear relations in these spaces.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1984
Synopsis For a symmetric linear relation S with a directing mapping, the notion of a spectral fun... more Synopsis For a symmetric linear relation S with a directing mapping, the notion of a spectral function is defined by means of a BesselParseval inequality, and a description of all such spectral functions is given. As an application, we describe the set of all spectral functions ...
... 250 Math. Nachr. 162 (1993) Remark 2. In the situation of Remark 1, if 8 is a regular unitary... more ... 250 Math. Nachr. 162 (1993) Remark 2. In the situation of Remark 1, if 8 is a regular unitary dilation of T (see [AI], V.3), then llYT = 01.9,. and T'1.9,. = 0'1%. Indeed, if x E YT we have [x, x] = [Tx, Tx] = [POX, POX] I [Ox, Ox] [x, XI, hence Tx=Pox=oxandx=T+Zk=T+ox. Proposition 1.5. ...
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