## Linear Operators: Spectral theory |

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Page 1472

τσ least one such

independent

all

that for any ...

τσ least one such

**solution**must exist . On the other hand , if two linearlyindependent

**solutions**of to = lo satisfy the boundary condition B , it follows thatall

**solutions**of to = ho satisfy B. By the remark ( a ) made above , it then followsthat for any ...

Page 1521

Putting yo = 1 / 2 + i so that ho = 1 + i , we see that the equation ( L - 2 ) has one

. The

Putting yo = 1 / 2 + i so that ho = 1 + i , we see that the equation ( L - 2 ) has one

**solution**of the order of t - 1 - i as t = 0 and another which behaves like t ' as t → 00. The

**solution**at ho = 1 - i is exactly similar . Thus , by Theorem XII.4.19 , L , -a ...Page 1529

Then in this angle any

with the factor exp ( 511 ) k - 1 ) is exponentially small ( as 121 + 0 in the angle )

relative to any

Then in this angle any

**solution**of L1 = 0 whose asymptotic expansion beginswith the factor exp ( 511 ) k - 1 ) is exponentially small ( as 121 + 0 in the angle )

relative to any

**solution**whose asymptotic expansion begins with the factor exp ...### What people are saying - Write a review

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