Eigenvalues and Eigenfunctions of a Class of Potential Operators in the Plane |
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Page 27
... vanishes at infinity as Iz1 . At At D its normal derivatives from either side are defined and satisfy ( 1.310 ) In By Green's identity , we transform the following Dirichlet integrals into boundary integrals : ( 1.311 ) Į ( vv ) 2 atz ...
... vanishes at infinity as Iz1 . At At D its normal derivatives from either side are defined and satisfy ( 1.310 ) In By Green's identity , we transform the following Dirichlet integrals into boundary integrals : ( 1.311 ) Į ( vv ) 2 atz ...
Page 28
... vanish and we conclude that ψ is constant in D and in D. But we know that is continuous and vanishes at infinity ; therefore it vanishes identically , and • = Q. Hence ( 1.36 ) becomes λφ ( 2 ) = λφ ( 2 ) = 3 = √ B2 ( 2,5 ) Q ( 5 ) at ...
... vanish and we conclude that ψ is constant in D and in D. But we know that is continuous and vanishes at infinity ; therefore it vanishes identically , and • = Q. Hence ( 1.36 ) becomes λφ ( 2 ) = λφ ( 2 ) = 3 = √ B2 ( 2,5 ) Q ( 5 ) at ...
Page 82
... vanishes at infinity and on D , and so by the maximum principle , vanishes identically in D. From the analyticity and behavior near in- finity of the ratio , we conclude that and so ( 2.420 ) reduces to ( 2.422 ) Moreover , 2 2 in D , 2 ...
... vanishes at infinity and on D , and so by the maximum principle , vanishes identically in D. From the analyticity and behavior near in- finity of the ratio , we conclude that and so ( 2.420 ) reduces to ( 2.422 ) Moreover , 2 2 in D , 2 ...
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