id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-938	Borisov, D.	On a Quantum Waveguide with a Small PT-symmetric Perturbation	2007	3	.pdf	application/pdf	1683	84	73	that if Re k1 0� , or Re k1 0� , Re k2 0� , (7) there exists the unique eigenvalue of �� converging to the threshold of the continuous spectrum, and the asymptotics of this eigenvalue reads as follows � � � �� � �� � � � 1 02 1 2 2 3k In this case ~V � 0, ~u � 0 and K u L� � � 1 2 01 2 2( )� (12) If the relation (6) holds true, the function u1 is identically zero, and K V u L: (~,~) ( )� � 2 � Employing (3), by analogy with (11) in the same way we check ~~ ~ ~ ( ) ( ) V u x u u L L d � � �� � � � 2 2	cache/ap-938.pdf	txt/ap-938.txt