Results 21 to 30 of about 468 (41)
The pseudodifferential operator A(x, D)
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 8, Page 407-419, 2004., 2004 The pseudodifferential operator (p.d.o.) A(x, D), associated with the Bessel operator d2/dx2 + (1 − 4μ2)/4x2, is defined. Symbol class Hρ,δm is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space Hμ into itself. An integral representation of p.d.o.
R. S. Pathak, S. Pathak
wiley +1 more source
The algebraic size of the family of injective operators
Open Mathematics, 2017 In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach
Bernal-González Luis
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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 53, Page 2821-2834, 2004., 2004 We extend the Putnam‐Fuglede theorem and the second‐degree Putnam‐Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpotents. Some asymptotic results are also given.
Yin Chen
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Every Hilbert space frame has a Naimark complement [PDF]
, 2002 Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual properties for
Casazza, Peter G. +4 more
core +9 more sources
Ill‐posed equations with transformed argument
Abstract and Applied Analysis, Volume 2003, Issue 13, Page 785-791, 2003., 2003 We discuss the operator transforming the argument of a function in the L2‐setting. Here this operator is unbounded and closed. For the approximate solution of ill‐posed equations with closed operators, we present a new view on the Tikhonov regularization.
Simone Gramsch, Eberhard Schock
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General numerical radius inequalities for matrices of operators
Open Mathematics, 2016 Let Ai ∈ B(H), (i = 1, 2, ..., n), and T=[0⋯0A1⋮⋰A200⋰⋰⋮An0⋯0] $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0
Al-Dolat Mohammed +3 more
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A note on best approximation and invertibility of operators on uniformly convex Banach spaces
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 3, Page 611-614, 1991., 1991 It is shown that if X is a uniformly convex Banach space and S a bounded linear operator on X for which ‖I − S‖ = 1, then S is invertible if and only if . From this it follows that if S is invertible on X then either (i) dist(I, [S]) < 1, or (ii) 0 is the unique best approximation to I from [S], a natural (partial) converse to the well‐known sufficient
James R. Holub
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Joint numerical ranges: recent advances and applications minicourse by V. Müller and Yu. Tomilov
Concrete Operators, 2020 We present a survey of some recent results concerning joint numerical ranges of n-tuples of Hilbert space operators, accompanied with several new observations and remarks.
Müller V., Tomilov Yu.
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A new view of some operators and their properties in terms of the Non-Newtonian Calculus
Topological Algebra and its Applications, 2017 Differentiation and integration are basic operations of calculus and analysis. Indeed, they are in- finitesimal versions of substraction and addition operations on numbers, respectively.
Ünlüyol Erdal +2 more
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Closable Hankel operators and moment problems
, 2019 In a paper from 2016 D. R. Yafaev considers Hankel operators associated with Hamburger moment sequences q_n and claims that the corresponding Hankel form is closable if and only if the moment sequence tends to 0.
Berg, Christian, Szwarc, Ryszard
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