scholarly journals Exterior Powers and Pointwise Creation Operators

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Dimitrios Chiotis ◽  
Zinaida A. Lykova ◽  
N. J. Young
Keyword(s):  
Operator Theory ◽  
Analytic Functions ◽  
Unit Disc ◽  
Nehari Problem ◽  
New Approach ◽  
Exterior Powers ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Creation Operators

AbstractWe develop a theory of pointwise wedge products of vector-valued functions on the circle and the disc, and obtain results which give rise to a new approach to the analysis of the matricial Nehari problem. We investigate properties of pointwise creation operators and pointwise orthogonal complements in the context of operator theory and the study of vector-valued analytic functions on the unit disc.

scholarly journals On vector-valued Hardy martingales and a generalized Jensen's inequality

2003 ◽  
Vol 2003 (9) ◽  
pp. 527-532
Author(s):  
Annela R. Kelly ◽  
Brian P. Kelly
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Analytic Functions ◽  
Jensen’S Inequality ◽  
Monotonicity Property ◽  
Dual Group ◽  
Analytic Vector ◽  
Jensen's Inequality ◽  
Vector Valued Functions ◽  
Vector Valued

We establish a generalized Jensen's inequality for analytic vector-valued functions on𝕋Nusing a monotonicity property of vector-valued Hardy martingales. We then discuss how this result extends to functions on a compact abelian groupG, which are analytic with respect to an order on the dual group. We also give a generalization of Helson and Lowdenslager's version of Jensen's inequality to certain operator-valued analytic functions.

scholarly journals On a class of analytic functions related to Robertson’s formula and subordination

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Growth Theorem

AbstractIn this paper, we define and study a class of analytic functions in the unit disc by modification of the well-known Robertson’s analytic formula for starlike functions with respect to a boundary point combined with subordination. An integral representation and growth theorem are proved. Early coefficients and the Fekete–Szegö functional are also estimated.

Comparison of Judgment Scales of the Analytical Hierarchy Process — A New Approach

2019 ◽  
Vol 18 (02) ◽  
pp. 445-463 ◽  
Author(s):  
Klaus D. Goepel
Keyword(s):  
Analytical Hierarchy Process ◽  
Analytic Functions ◽  
Decision Problem ◽  
Decision Criteria ◽  
Maximum Weight ◽  
Analytic Hierarchy ◽  
New Approach ◽  
Scale Functions ◽  
Decision Method ◽  
Hierarchy Process

The analytic hierarchy process (AHP) remains a popular multi-criteria decision method. One topic under discussion of AHP is the use of different scales to translate judgments into ratios. The author makes a new approach to compare different scale functions and to derive a recommendation for the application of scales. The approach is based on simple analytic functions and takes into consideration the number of criteria of the decision problem. A generalization of the so-called balanced scale is proposed, and a new adaptive-balanced scale is introduced. Scales are then categorized and compared based on weight boundaries and weight ratios, weight uncertainties, weight dispersion and number of decision criteria. Finally, a practical example of a decision hierarchy is presented applying the different scales. The results show that the generalized balanced scale improves weight dispersion and weight uncertainty in comparison to the fundamental AHP scale. The proposed adaptive-balanced scale overcomes the problem of a change of the maximum weight depending on the number of decision criteria.

scholarly journals Farkas-Type Results for Vector-Valued Functions with Applications

2017 ◽  
Vol 173 (2) ◽  
pp. 357-390 ◽  
Author(s):  
N. Dinh ◽  
M. A. Goberna ◽  
M. A. López ◽  
T. H. Mo
Keyword(s):  
Vector Valued Functions ◽  
Vector Valued

scholarly journals A coefficient inequality for the class of analytic functions in the unit disc

2003 ◽  
Vol 2003 (59) ◽  
pp. 3753-3759
Author(s):  
Yaşar Polatoğlu ◽  
Metın Bolcal
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Coefficient Inequality

The aim of this paper is to give a coefficient inequality for the class of analytic functions in the unit discD={z||z| <1}.

scholarly journals Diameter-preserving linear bijections of function spaces

2001 ◽  
Vol 70 (3) ◽  
pp. 323-336 ◽  
Author(s):  
T. S. S. R. K. Rao ◽  
A. K. Roy
Keyword(s):  
Maximal Ideal ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Continuous Functions ◽  
Ideal Space ◽  
Function Algebras ◽  
Compact Convex Set ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractIn this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.

scholarly journals THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS

2014 ◽  
Vol 57 (1) ◽  
pp. 17-82 ◽  
Author(s):  
TUOMAS P. HYTÖNEN ◽  
ANTTI V. VÄHÄKANGAS
Keyword(s):  
Singular Integrals ◽  
Local Version ◽  
Square Functions ◽  
Property A ◽  
Martingale Differences ◽  
Umd Spaces ◽  
Function Lattice ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Similar Extension

AbstractWe extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, ‘vector-valued’ means ‘taking values in a function lattice with the UMD (unconditional martingale differences) property’. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.

Strict Topologies for Vector-Valued Functions

1974 ◽  
Vol 26 (4) ◽  
pp. 841-853 ◽  
Author(s):  
Robert A. Fontenot
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Measure Theory ◽  
Strict Topology ◽  
Locally Compact ◽  
Topological Measure ◽  
Topological Measure Theory ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space

This paper is motivated by work in two fields, the theory of strict topologies and topological measure theory. In [1], R. C. Buck began the study of the strict topology for the algebra C*(S) of continuous, bounded real-valued functions on a locally compact Hausdorff space S and showed that the topological vector space C*(S) with the strict topology has many of the same topological vector space properties as C0(S), the sup norm algebra of continuous realvalued functions vanishing at infinity. Buck showed that as a class, the algebras C*(S) for S locally compact and C*(X), for X compact, were very much alike. Many papers on the strict topology for C*(S), where S is locally compact, followed Buck's; e.g., see [2; 3].

HOMOMORPHISMS OF BANACH ALGEBRAS WITH RANGE IN C1[0, 1]

1994 ◽  
Vol 05 (02) ◽  
pp. 201-212 ◽  
Author(s):  
HERBERT KAMOWITZ ◽  
STEPHEN SCHEINBERG
Keyword(s):  
Analytic Functions ◽  
Compact Hausdorff Space ◽  
Unit Disc ◽  
Hausdorff Space ◽  
Banach Algebras ◽  
Locally Compact ◽  
Disc Algebra ◽  
Uniform Algebras ◽  
Closed Subalgebra ◽  
Uniformly Closed

Many commutative semisimple Banach algebras B including B = C (X), X compact, and B = L1 (G), G locally compact, have the property that every homomorphism from B into C1[0, 1] is compact. In this paper we consider this property for uniform algebras. Several examples of homomorphisms from somewhat complicated algebras of analytic functions to C1[0, 1] are shown to be compact. This, together with the fact that every homomorphism from the disc algebra and from the algebra H∞ (∆), ∆ = unit disc, to C1[0, 1] is compact, led to the conjecture that perhaps every homomorphism from a uniform algebra into C1[0, 1] is compact. The main result to which we devote the second half of this paper, is to construct a compact Hausdorff space X, a uniformly closed subalgebra [Formula: see text] of C (X), and an arc ϕ: [0, 1] → X such that the transformation T defined by Tf = f ◦ ϕ is a (bounded) homomorphism of [Formula: see text] into C1[0, 1] which is not compact.

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