scholarly journals Eigenfunction expansions associated with second-order differential equations for Hilbert space-valued functions

1971 ◽  
Vol 7 (1) ◽  
pp. 1-55 ◽  
Author(s):  
Saitō Yoshimi Saitō Yoshimi
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Second Order ◽  
Eigenfunction Expansions ◽  
Second Order Differential Equations

On the growth of solutions to second order differential equations in Banach spaces

1985 ◽  
Vol 101 (3-4) ◽  
pp. 237-252 ◽  
Author(s):  
H. O. Fattorini
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Complex Number ◽  
Exponential Growth ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Arbitrary Complex Number ◽  
Arbitrary Complex ◽  
Growth Of Solutions

SynopsisWe obtain estimates for the exponential growth of the solutions to u″(t) = (A + ζ2I)u(t) in terms of the exponential growth of the solutions to u″(t) = Au(t), where ζ is an arbitrary complex number. Estimates in exponentially weighted L2 norms are also considered in Hilbert space.

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