The Phragmén-Lindelöf theorem for regular functional cochains

1991 ◽  
pp. 121-158
Keyword(s):  
Lindelöf Theorem ◽  
Regular Functional

scholarly journals On a Counterexample in Connection with the Picard-Lindelöf Theorem

2021 ◽  
Vol 52 (3) ◽  
pp. 221-223
Author(s):  
Georgios Passias ◽  
Sven-Ake Wegner
Keyword(s):  
Lindelöf Theorem

scholarly journals Potential theoretic properties of the gradient of a convex function on a functional space

1975 ◽  
Vol 59 ◽  
pp. 199-215 ◽  
Author(s):  
Nobuyuki Kenmochi ◽  
Yoshihiro Mizuta
Keyword(s):  
Maximum Principle ◽  
Convex Function ◽  
Functional Space ◽  
Monotone Operators ◽  
Lower Envelope ◽  
Real Interval ◽  
List Type ◽  
Strong Principle ◽  
Complete Maximum Principle ◽  
Regular Functional

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.

A Regular Singular Functional

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].

The generalized Laguerre inequalities and functions in the Laguerre-Pólya class

2013 ◽  
Vol 11 (9) ◽  
Author(s):  
George Csordas ◽  
Anna Vishnyakova
Keyword(s):  
Entire Function ◽  
Open Problem ◽  
A Priori ◽  
Sufficient Conditions ◽  
Class Definition ◽  
Lindelöf Theorem ◽  
Order And Type ◽  
Geometric Result ◽  
Real Entire Function ◽  
Inequality Theorem

AbstractThe principal goal of this paper is to show that the various sufficient conditions for a real entire function, φ(x), to belong to the Laguerre-Pólya class (Definition 1.1), expressed in terms of Laguerre-type inequalities, do not require the a priori assumptions about the order and type of φ(x). The proof of the main theorem (Theorem 2.3) involving the generalized real Laguerre inequalities, is based on a beautiful geometric result, the Borel-Carathédodory Inequality (Theorem 2.1), and on a deep theorem of Lindelöf (Theorem 2.2). In case of the complex Laguerre inequalities (Theorem 3.2), the proof is sketched for it requires a slightly more delicate analysis. Section 3 concludes with some other cognate results, an open problem and a conjecture which is based on Cardon’s recent, ingenious extension of the Laguerre-type inequalities.

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