Riesz Projection and Essential S-spectrum in Quaternionic Setting
نویسندگان
چکیده
This paper is devoted to the investigation of Weyl and essential S-spectra a bounded right quaternionic linear operator in Hilbert space. Using Riesz projection, S-eigenvalue finite type both introduced studied. In particular, we have shown that do not contain eigenvalues type. We also described boundary S-spectrum particular case spectral theorem S-spectrum.
منابع مشابه
Quaternionic Representation of the Riesz Pyramid for Video Magnification
Recently, we presented a new image pyramid, called the Riesz pyramid, that uses the Riesz transform to manipulate the phase in non-oriented sub-bands of an image sequence to produce real-time motion-magnified videos. In this report we give a quaternionic formulation of the Riesz pyramid, and show how several seemingly heuristic choices in how to use the Riesz transform for phase-based video mag...
متن کاملMöbius Transformations and the Poincaré Distance in the Quaternionic Setting
In the space H of quaternions, we investigate a natural, invariant geometry of the open, unit disc ∆H and of the open half-space H . These two domains are diffeomorphic via a Cayley-type transformation. We first study the geometrical structure of the groups of Möbius transformations of ∆H and H + and identify original ways of representing them in terms of two (isomorphic) groups of matrices wit...
متن کاملThe Orthogonal Projection and the Riesz Representation Theorem
In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real ...
متن کاملThe Heat Kernel and the Riesz Transforms on the Quaternionic Heisenberg Groups
As the heat kernel plays an important role in many problems in harmonic analysis, an explicit usable expression is very much desirable. An explicit expression for the heat kernel for the Heisenberg group Hn = C ×R was obtained by Hulanicki [9] and by Gaveau [7]. Gaveau [7] also obtained the heat kernel for free nilpotent Lie groups of step two. Cygan [4] obtained the heat kernel for all nilpote...
متن کاملBoundedness of the Riesz Projection on Spaces with Weights
Let ∂D be the unit circle in the complex plane, define the function χ on ∂D by χ(eiθ) = eiθ, and set P = {p : p = ∑Nk=−N ckχ}. Let σ be normalized Lebesgue measure on ∂D. The Riesz projection P+ is defined on P by the formula P+( ∑N k=−N ckχ k) = ∑N k=0 ckχ k. In [4], Paul Koosis proved: Theorem 1 (Koosis). Given a non-negative function w ∈ L1, there exists a non-negative, non-trivial function ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Complex Analysis and Operator Theory
سال: 2022
ISSN: ['1661-8254', '1661-8262']
DOI: https://doi.org/10.1007/s11785-022-01276-x