There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Real and Complex Analysis

General Theory of Banach Algebra. By C.E. Rickart. Pp. 394. 79s. 1960. (Van Nostrand, London)

What do you do to start reading dimension theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this dimension theory.

Aspects of topology: On dimension theory

Functions of One Complex Variable

The problem of the simultaneous stabilizability of a finite family of single-input, single-output time-invariant systems by a time- invariant controller is studied. The link between stabilization and avoidance is shown and is used to derive necessary conditions for the simultaneous stabilization of k plants. These necessary conditions are proved to be, in general, not sufficient. This result also disproves a long- standing conjecture on the stabilizability condition of a single plant with a stable minimum phase controller. The main result is to show that, unlike the case of two plants, the existence of a simultaneous stabilizing controller for more than two plants is not guaranteed by the existence of a controller such that the closed loops have no real unstable poles.

Simultaneous Stabilization of Three or More Plants: Conditions on the Positive Real Axis Do Not Suffice

For sequences (φ
 n
 ) of eventually injective holomorphic self-maps of planar domains Ω, we present necessary and sufficient conditions for the existence of holomorphic functions f on whose orbits under the action of (φ
 n
 ) are dense in H (Ω). It is deduced that finitely connected, but non-simply connected domains never admit such universal functions. On the other hand, if we allow arbitrary sequences of holomorphic self-maps (φ
 n
 ), the situation changes dramatically.

Universal functions for composition operators with non-automorphic symbol

Ellipses and Finite Blaschke Products

T. Hosokawa, K. Izuchi and D. Zheng recently introduced the concept of asymptotic interpolating sequences (of type 1) in the unit disk for on arbitrary domains is verified. It is shown that any asymptotic interpolating sequence in a uniform algebra eventually is interpolating.

Asymptotic interpolating sequences in uniform algebras

https://projecteuclid.org/download/pdf_1/euclid.mmj/1029004270

Raymond Mortini

Papers

Simultaneous Stabilization of Three or More Plants: Conditions on the Positive Real Axis Do Not Suffice

Universal functions for composition operators with non-automorphic symbol

Ellipses and Finite Blaschke Products

Asymptotic interpolating sequences in uniform algebras

Interpolating Blaschke products and factorization in Douglas algebras.