We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.
@article{JEDP_2001____A8_0, author = {Jak\v{s}i\'c, Vojkan}, title = {Spectral theory of corrugated surfaces}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {8}, pages = {1--11}, publisher = {Universit\'e de Nantes}, year = {2001}, doi = {10.5802/jedp.592}, mrnumber = {1843409}, zbl = {1029.39021}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.592/} }
Jakšić, Vojkan. Spectral theory of corrugated surfaces. Journées équations aux dérivées partielles (2001), article no. 8, 11 p. doi : 10.5802/jedp.592. http://www.numdam.org/articles/10.5802/jedp.592/
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