## Eigenvalues and Eigenfunctions of a Class of Potential Operators in the Plane |

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Page 55

such that \ "k almost

cp "k by kup and conclude that almost

everywhere in E and X \|r -» X cp pointwise and boundedly on A , since cp,\|r e ...

such that \ "k almost

**uniformly**in E. Moreover, since u -» H < 0, we may replacecp "k by kup and conclude that almost

**uniformly**in E. Hence cp is non-negativeeverywhere in E and X \|r -» X cp pointwise and boundedly on A , since cp,\|r e ...

Page 61

... using the integral representation of t+h ~5T obtained by differentiating (2.3*0

under the integral, it is easily shown that the derivative term is bounded by a

constant in A , and hence the entire expression (2.37) is o(l)

result, ...

... using the integral representation of t+h ~5T obtained by differentiating (2.3*0

under the integral, it is easily shown that the derivative term is bounded by a

constant in A , and hence the entire expression (2.37) is o(l)

**uniformly**in A. As aresult, ...

Page 66

It is clear that such functions F(z) do exist; for instance, define (2.41) { F(z) = F(z) =

ia e ia e ^=1 exp |z-C -P for |z-^| < p for z-^| > p ^ w=z+pF(z) As p 10, the domains

D* X£ D; hence, by Theorem 2.k, \|r*(w) -» ^(w) almost

It is clear that such functions F(z) do exist; for instance, define (2.41) { F(z) = F(z) =

ia e ia e ^=1 exp |z-C -P for |z-^| < p for z-^| > p ^ w=z+pF(z) As p 10, the domains

D* X£ D; hence, by Theorem 2.k, \|r*(w) -» ^(w) almost

**uniformly**in E, and so ...### What people are saying - Write a review

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