The Hankel Transformation of Certain Distributions of Rapid Growth

Zemanian, A. H.

doi:10.1137/0114056

Cited by 65 publications

(27 citation statements)

References 4 publications

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“…By a theorem due to Griffith [Gri55] (see also [Zem66]), which is to some extend a generalization of the Paley-Wiener theorem but involving the Hankel transform, one has…”

Section: Spaces Of Polynomials Consider the Linear Setmentioning

confidence: 99%

de Branges Spaces and Krein’s Theory of Entire Operators

Silva

Toloza

2014

Operator Theory

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This work presents a contemporary treatment of Krein's entire operators with deficiency indices (1, 1) and de Branges' Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown mathematicians. Remarkably, entire operators and de Branges spaces are intimately connected and the interplay between them has had an impact in both spectral theory and the theory of functions. This work exhibits the interrelation between Krein's and de Branges' theories by means of a functional model and discusses recent developments, giving illustrations of the main objects and applications to the spectral theory of difference and differential operators.Mathematics Subject Classification(2010): 46E22; Secondary 47A25, 47B25, 47N99.

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“…By a theorem due to Griffith [Gri55] (see also [Zem66]), which is to some extend a generalization of the Paley-Wiener theorem but involving the Hankel transform, one has…”

Section: Spaces Of Polynomials Consider the Linear Setmentioning

confidence: 99%

de Branges Spaces and Krein’s Theory of Entire Operators

Silva

Toloza

2014

Operator Theory

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show abstract

“…Jo where, as usual, J^ denotes the Bessel function of the first kind and order ji, was studied on distribution spaces by A. H. Zemanian [14], [15]. Given /i G IR, this author [15,Chapter 5] The theory of the Hankel convolution on Jr^, 38^, and their duals has been developed by the authors in a series of papers [2], [3], [4], [10].…”

Section: /•Oo (F)y -\)mentioning

confidence: 99%

Convolution operators on Kucera-type spaces for the Hankel transformation

Marrero

1997

Czechoslovak Mathematical Journal

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“…Moreover h^ is an automorphism of #f M provided that /x > -1/2. For every a > 0, A. H. Zemanian [15] defined the space /3^0 as follows: a complex valued and smooth function 4>(x), (x E /), is in B^a if and only if (f> e #? M and <p(x) = 0, for every x ^ a.…”

Section: •>0mentioning

confidence: 99%

“…The space /3^ = U )3 M , O is endowed with the inductive limit topology. The Hankel transform of /3 M is characterized in [15].…”

Section: •>0mentioning

confidence: 99%