Hi, I'm reading "Spectral Theory of Linear Operators" by John Dowson. I've seen the phrase "analytic at infinity" popping up very early in the book, but no definition is given. I wonder if anyone could tell me what the definition is or where I might find the definition and perhaps a few basic results on analyticity at infinity? The operators I'm looking at are continuous linear maps from a complex Banach space to itself, so my question is really about complex analysis. I've tried Google but have found no definition. I think "bounded at infinity" is a related concept, but again I do not know what that means. Maybe someone can help me out there too? Thanks.