✦ LIBER ✦

Invertible Convolutions

✍ Scribed by Edgar Berz

Publisher: John Wiley and Sons
Year: 1975
Tongue: English
Weight: 295 KB
Volume: 66
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19750660103

No coin nor oath required. For personal study only.

✦ Synopsis

As is well known, the finite distributions on Rn form an algebra t 5 ' with respect to the convolution-product ; DIRAC'S measure 6 is the unit of this algebra.

We propose to determine the invertible elements in this algebra.

The algebra &"(*) is isomorphic to the algebra &(a') of the continuous linear operators A : B ' 4 B ' of the distribution-space B', which commute with all translations. Therefore the knowledge of the invertible S E 8" leads to the invertible operators A € &(a'). It turns out, that these are exactly the translations and the non-zero multiples of them.

📜 SIMILAR VOLUMES

On the Structure of Invertible Elements

On the Structure of Invertible Elements of the Convolution Algebra S′k

✍ B.J. Gonzalez; E.R. Negrin 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 317 KB

Generalized Convolutions

✍ Lothar Berg 📂 Article 📅 1976 🏛 John Wiley and Sons 🌐 English ⚖ 283 KB

Invertible Toeplitz Products

✍ Karel Stroethoff; Dechao Zheng 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 192 KB

We will discuss invertibility of Toeplitz products T f T % g g ; for analytic f and g; on the Bergman space and the Hardy space. We will furthermore describe when these Toeplitz products are Fredholm.

Topology and Invertible Maps

✍ Graciela Chichilnisky 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 151 KB

Invertible Sharplyn-Transitive Sets

✍ Burkard Polster 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 509 KB

We prove various results about sharply n-transitive sets of homeomorphisms of ``nice'' topological spaces like the real line and the circle. Our main results concern sharply 3-transitive sets G of homeomorphisms of the circle to itself. If G=G &1 , then G contains a real hyperbolic part (a set of in

Non-invertible knots exist

✍ H.F. Trotter 📂 Article 📅 1963 🏛 Elsevier Science 🌐 English ⚖ 334 KB