carleman kernel
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2012 ◽  
Vol 53 (6) ◽  
pp. 1011-1020 ◽  
Author(s):  
F. N. Garif’yanov ◽  
S. A. Modina
Keyword(s):  

1972 ◽  
Vol 15 (1) ◽  
pp. 129-131
Author(s):  
Charles G. Costley

The celebrated Fredholm theory of linear integral equations holds if the kernel K(x, y) or one of its iterates K(n) is bounded. Hilbert utilizing his theory of quadratic form was able to extend the theory to the kernels K(x, y) satisfyingabwhere k is independent of u(x).These theories were extended considerably by T. Carleman who deleted condition (b) above.Equations involving this Carleman kernel have been found useful in connection with Hermitian forms, continued fractions, Schroedinger wave equations (see [1], [2]) and more recently in scattering theory in quantum physics, etc. [3]. See also [5] for a variety of applications and extensions.


1970 ◽  
Vol 13 (4) ◽  
pp. 415-421
Author(s):  
Charles G. Costley

We consider here the equation1This equation was first studied by Hammerstein [4] under the assumption that the linear operator2is selfadjoint and completely continuous. V. Nemytsky [5] and M. Golomb [3] dropped the assumption that A be selfadjoint and positive. M. Vainberg [6] considered (among other cases) the case in which A is a bounded operator generated by a Carleman kernel. The kernels considered in this work do not necessarily generate bounded, completely continuous or selfadjoint, operators.


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