scholarly journals Comparison theorems for Banach spaces of solutions of $\Delta u=Pu$ on Riemann surfaces

1979 ◽  
Vol 31 (2) ◽  
pp. 281-316 ◽  
Author(s):  
Takeyoshi SATO
Keyword(s):  
Banach Spaces ◽  
Riemann Surfaces ◽  
Comparison Theorems

scholarly journals Banach spaces of bounded solutions of Δu = Pu (P ≥ 0) on hyperbolic riemann surfaces

1974 ◽  
Vol 53 ◽  
pp. 141-155 ◽  
Author(s):  
Mitsuru Nakai
Keyword(s):  
Banach Space ◽  
Riemann Surface ◽  
Banach Spaces ◽  
Riemann Surfaces ◽  
Space Structure ◽  
Bounded Solutions ◽  
Linear Isometry ◽  
Hölder Continuous ◽  
Hyperbolic Riemann Surfaces ◽  
Hyperbolic Riemann Surface

Consider a nonnegative Hölder continuous 2-form P(z)dxdy on a hyperbolic Riemann surface R (z = x + iy). We denote by PB(R) the Banach space of solutions of the equation Δu = Pu on R with finite supremum norms. We are interested in the question how the Banach space structure of PB(R) depends on P. Precisely we consider two such 2-forms P and Q on R and compare PB(R) and QB(R). If there exists a bijective linear isometry T of PB(R) to QB(R), then we say that PB(R) and QB(R) are isomorphic.

scholarly journals On summation processes of Fourier expansions in Banach spaces, I. Comparison theorems

1972 ◽  
Vol 24 (2) ◽  
pp. 127-140 ◽  
Author(s):  
P. L. Butzer ◽  
R. J. Nessel ◽  
W. Trebels
Keyword(s):  
Banach Spaces ◽  
Comparison Theorems ◽  
Fourier Expansions
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