AUTOMATON PROGRAMS AND REGULAR FUNCTIONAL EXPRESSIONS-ON AN EXTENSION OF DERIVATIVES

In the previous paper [11], introducing the notions of potentials and of capacity associated with a convex function Φ given on a regular functional space we discussed potential theoretic properties of the gradient ∇Φ which were originally introduced and studied by Calvert [5] for a class of nonlinear monotone operators in Sobolev spaces. For example: (i)The modulus contraction operates.(ii)The principle of lower envelope holds.(iii)The domination principle holds.(iv)The contraction Tk onto the real interval [0, k] (k > 0) operates.(v)The strong principle of lower envelope holds.(vi)The complete maximum principle holds.

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Dirichlet forms on regular functional spaces

Seminar on Potential Theory, II - Lecture Notes in Mathematics ◽

10.1007/bfb0060480 ◽

1971 ◽

pp. 15-62 ◽

Cited By ~ 11

Author(s):

Jürgen Bliedtner

Keyword(s):

Dirichlet Forms ◽

Regular Functional

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A Regular Singular Functional

Canadian Journal of Mathematics ◽

10.4153/cjm-1956-010-x ◽

1956 ◽

Vol 8 ◽

pp. 53-68

Author(s):

A. D. Martin

Keyword(s):

Singular Point ◽

Closed Interval ◽

Joint Paper ◽

Quadratic Functionals ◽

Image Position ◽

Regular Functional

1. Introduction. In a joint paper with Leighton (2), the author considered quadratic functionals of the type1.1 (0 < a < b)in which x = 0 is a singular point of the functional which is otherwise regular on [0, b]. The hypothesis on a regular functional includes the assumption that r is continuous and positive on a closed interval [0, b].

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On the impact of regular functional dependencies when moving to a possibilistic database framework

Fuzzy Sets and Systems ◽

10.1016/s0165-0114(02)00530-4 ◽

2003 ◽

Vol 140 (1) ◽

pp. 207-227 ◽

Cited By ~ 16

Author(s):

Patrick Bosc ◽

Olivier Pivert

Keyword(s):

Functional Dependencies ◽

The Impact ◽

Regular Functional

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Condensor Principle and the Unit Contraction

Nagoya Mathematical Journal ◽

10.1017/s0027763000012319 ◽

1967 ◽

Vol 30 ◽

pp. 9-28 ◽

Cited By ~ 3

Author(s):

Masayuki Itô

Keyword(s):

Positive Measure ◽

Hausdorff Space ◽

Sufficient Conditions ◽

Dirichlet Space ◽

Functional Space ◽

Dirichlet Spaces ◽

Locally Compact ◽

Necessary And Sufficient ◽

Regular Functional ◽

Locally Compact Hausdorff Space

Deny introduced in [4] the notion of functional spaces by generalizing Dirichlet spaces. In this paper, we shall give the following necessary and sufficient conditions for a functional space to be a real Dirichlet space.Let be a regular functional space with respect to a locally compact Hausdorff space X and a positive measure ξ in X. The following four conditions are equivalent.

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