Transactions of the Cambridge Philosophical Society, المجلد 22University Press, 1923 |
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الصفحة 133
... parameter values . VIII . The conjugo - symmetric dyadic kernel . 148 153 INTRODUCTION . THE integral equations that have hitherto been considered by mathematicians are scalar equations in which the functions involved are not related to ...
... parameter values . VIII . The conjugo - symmetric dyadic kernel . 148 153 INTRODUCTION . THE integral equations that have hitherto been considered by mathematicians are scalar equations in which the functions involved are not related to ...
الصفحة 138
... parameter λ , be used to obtain the solution of our standard equation u ( t ) − λ [ K ( ts ) • u ( s ) ds = f ( t ) - . ( 1 ) . For on substituting for u ( s ) under the integral sign the value given by the equation itself , we deduce ...
... parameter λ , be used to obtain the solution of our standard equation u ( t ) − λ [ K ( ts ) • u ( s ) ds = f ( t ) - . ( 1 ) . For on substituting for u ( s ) under the integral sign the value given by the equation itself , we deduce ...
الصفحة 139
... parameter values than this . We shall prove that if there exists a dyadic H ( ts ) connected with K ( ts ) by the relation ( 11 ) then the integral equation ( 1 ) admits a unique solution given by For on multiplying u ( t ) = f ( t ) + ...
... parameter values than this . We shall prove that if there exists a dyadic H ( ts ) connected with K ( ts ) by the relation ( 11 ) then the integral equation ( 1 ) admits a unique solution given by For on multiplying u ( t ) = f ( t ) + ...
الصفحة 140
... parameter λ , and to extend the validity of the solutions ( 12 ) and ( 13 ) to the case in which the parameter value is quite general , we shall endeavour to find a resolvent dyadic H ( ts ) satisfying the relations ( 11 ) and ( 11 ...
... parameter λ , and to extend the validity of the solutions ( 12 ) and ( 13 ) to the case in which the parameter value is quite general , we shall endeavour to find a resolvent dyadic H ( ts ) satisfying the relations ( 11 ) and ( 11 ...
الصفحة 143
... parameter λ , and that the vector integral equation ( 1 ) is equivalent to the system ( 2 ) which in turn can be replaced by the single integral equation ( 5 ) , we are prepared to find the solution u ( t ) of ( 1 ) also a meromorphic ...
... parameter λ , and that the vector integral equation ( 1 ) is equivalent to the system ( 2 ) which in turn can be replaced by the single integral equation ( 5 ) , we are prepared to find the solution u ( t ) of ( 1 ) also a meromorphic ...
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