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Besides, it is a Nevanlinna analytic operator function in λ on the set of regular points of Lint . In particular, DN int takes self-adjoint values for real regular λ. More about modern DN-techniques and its applications in spectral analysis can be found in [16, 17, 18, 19, 20]. In this paper we study connection between the one-body scattering 8 V. Adamyan, B. Pavlov and A. Yafyasov matrix and the DN-map on the two-dimensional junction. For “thin” junctions the connection is used in transport problems in [11, 21, 22].

Geom. Phys. 541 (2005), 77–115. [8] J. Gabelli, G. -M. Berroir, B. Placais, A. Cavanna, B. Etienne, Y. C. Glatti, Violation of Kirchhoff ’s Laws for a coherent RC Cirquit. Science 313 (2006), 499–502. [9] O. Madelung. Introduction to solid-state theory. C. Taylor. Springer Series in Solid-State Sciences, 2. Springer-Verlag, Berlin, New York, 1978. [10] M. Harmer, B. Pavlov, A. Yafyasov Boundary conditions at the junction. International Workshop on Computational Electronics (IWCE-11), Vienna, 25 May–29 May 2006, book of abstracts, 241–242.

Unfortunately this breeding can’t be interpreted only in terms of the spectral theory of self-adjoint operators. Nevertheless we are able to suggest an algebraic version of the analysis of this breeding, based on the corresponding Krein formula. 3. Krein formula for the scattering matrix Krein formula for the scattering matrix which corresponds to the generalized resolvent of a general symmetric operator was obtained first in [27]. In [28] this formula was used in analysis of zero-range solvable models.

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