The relation between the bounded point derivation and the fine derivation

1988 ◽  
pp. 252-264
Author(s):  
Nguyen Xuan-Loc
Keyword(s):  
Point Derivation

scholarly journals Object-Oriented Type Inference

1991 ◽  
Vol 20 (345) ◽  
Author(s):  
Jens Palsberg ◽  
Michael I. Schwartzbach
Keyword(s):  
Fixed Point ◽  
Object Oriented ◽  
Type Inference ◽  
Finite Sets ◽  
New Approach ◽  
Optimizing Compiler ◽  
Point Derivation ◽  
Set Inclusion ◽  
Least Solution ◽  
Type Information

We present a new approach to inferring types in untyped object-oriented programs with inheritance, assignments, and late binding. It guarantees that all messages are understood, annotates the program with type information, allows polymorphic methods, and can be used as the basis of an optimizing compiler. Types are finite sets of classes and subtyping is set inclusion. Using a trace graph, our algorithm constructs a set of conditional type constraints and computes the least solution by least fixed-point derivation.

scholarly journals Higher point derivations on commutative Banach algebras, III

1981 ◽  
Vol 24 (1) ◽  
pp. 31-40 ◽  
Author(s):  
H. G. Dales ◽  
J. P. McClure
Keyword(s):  
Banach Algebra ◽  
Infinite Order ◽  
Infinite Sequence ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Complex Field ◽  
Linear Functionals ◽  
Point Derivation ◽  
Commutative Banach Algebras ◽  
Image Position

Let A be a commutative Banach algebra with identity 1 over the complex field C, and let d0 be a character on A. We recall that a (higher) point derivation of order q on A at d0 is a sequence d1, …, dq of linear functionals on A such that the identitieshold for each choice of f and g in A and k in {1, …, q}. A point derivation of infinite order is an infinite sequence {dk} of linear functionals such that (1.1) holds for all k. A point derivation is continuous if each dk is continuous, totally discontinuous if dk is discontinuous for each k≧1, and degenerate if d1 = 0.

scholarly journals An isolated bounded point derivation

1973 ◽  
Vol 39 (3) ◽  
pp. 559-559
Author(s):  
Anthony G. O’Farrell
Keyword(s):  
Point Derivation

An Isolated Bounded Point Derivation

1973 ◽  
Vol 39 (3) ◽  
pp. 559
Author(s):  
Anthony G. O'Farrell
Keyword(s):  
Point Derivation

scholarly journals A function algebra without any point derivation

1986 ◽  
Vol 111 (3) ◽  
pp. 230-234
Author(s):  
Krzysztof Jarosz ◽  
Zbigniew Sawoń
Keyword(s):  
Function Algebra ◽  
Point Derivation

scholarly journals Bounded point derivations on $R^p(X)$ and approximate derivatives

2019 ◽  
Vol 124 (1) ◽  
pp. 132-148
Author(s):  
Stephen Deterding
Keyword(s):  
Rational Function ◽  
Rational Functions ◽  
Higher Order ◽  
Point Derivation ◽  
Approximate Derivative

It is shown that if a point $x_0$ admits a bounded point derivation on $R^p(X)$, the closure of rational function with poles off $X$ in the $L^p(dA)$ norm, for $p >2$, then there is an approximate derivative at $x_0$. A similar result is proven for higher-order bounded point derivations. This extends a result of Wang which was proven for $R(X)$, the uniform closure of rational functions with poles off $X$.

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