Results 241 to 250 of about 2,695 (277)

Approximation of unbounded operators by bounded operators in a Hilbert space

Ukrainian Mathematical Journal, 2009
The authors find the best approximation of an arbitrary power \(A^k\) of an unbounded selfadjoint operator by bounded operators, on the class of elements \(\{ x\in D(A^r):\;\| A^rx\| \leq 1\}\), where \(r>k\). For the case of the differentiation operator \(A=i\frac{d}{dt}\) on \(L_2(\mathbb R)\), this gives the result by \textit{J. N.
V F Babenko
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The S-Functional Calculus for Unbounded Operators

, 2018
The Fueter mapping theorem in integral form introduced in [86], see Chapter 2.2, provides an integral transform that turns slice hyperholomorphic functions into Fueter regular ones. By formally replacing the scalar variable in this integral transform by an operator T, we obtain a functional calculus for Fueter regular functions that is based on the ...
Colombo F, Gantner J, Kimsey DP
core   +9 more sources

Bounded and Unbounded Linear Operators

2011
This chapter is devoted to the basic material on operator theory, semigroups, evolution familites, interpolation spaces, fractional powers of operators, intermediate spaces, and their basic properties needed in the sequel. Various illustrative examples are discussed in-depth. The estimates in Lemma 2.2 (Diagana et al. [52]) and Lemma 2.4 (Diagana [62])
Toka Diagana, Paul H Bezandry
exaly   +2 more sources

Linear differential operators with unbounded operator coefficients and semigroups of bounded operators

Mathematical Notes, 1996
Let \(X\) be a complex Banach space and \(L_p= L_p(R_+,X)\). The author considers the linear differential operator \[ {\mathcal L}= -{d\over dt}+ A(t): D({\mathcal L})\subset L_p\to L_p,\quad p\in[1,\infty] \] and studies its spectral properties under the assumption that the family of closed operators \(A(t): D(A(t))\subset X\to X\), \(t\geq 0 ...
A G Baskakov
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Best approximation of unbounded by bounded operators, and allied problems

Mathematical Notes, 1986
This paper contains the author's abstract of his Doctoral Dissertation. The dissertation is mainly concerned with best approximation in a certain class of elements of an in general unbounded operator by bounded linear operators. This problem is linked, among other extremal problems, with the problem of best restoration of operator values on elements of
Vitalii Arestov
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Bounded and Unbounded Linear Operators

1987
Let H be a complex inner product space and let L(H) be the set of all bounded linear operators on H. In this chapter we present some basic facts about the set L(H) as well as about the set of unbounded operators on H. We also present some classes of operators whose structure is better understood, among which we mention the class of hermitian, unitary ...
exaly   +2 more sources

On the Generation of Unbounded Semi-Groups of Bounded Linear Operators

Annals of Mathematics, 1953
William Feller
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On unbounded subnormal operators [PDF]

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 1989
A minimal normal extension of unbounded subnormal operators is established and characterized and spectral inclusion theorem is proved. An inverse Cayley transform is constructed to obtain a closed unbounded subnormal operator from a bounded one.
Patel, Arvind B., Bhatt, Subhash J.
exaly   +2 more sources

Representations of quadratic ∗-algebras by bounded and unbounded operators

Reports on Mathematical Physics, 1995
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Ostrovskyĭ, Vasyl L., Samoilenko, Yurii S.   +1 more
openaire   +1 more source

Bound, unbound operators and the squeezing effect

Il Nuovo Cimento B Series 11, 1995
In this paper we report the difference between the squeezing effect for quadrature operators (describing a photon field or harmonic oscillator) and for spin variables (describing a two-level system), the distinctions coming from the bound and unbound character of the operators involved in the definition of squeezing for each system.
B. Baseia, H. Dias, V. S. Bagnato
openaire   +1 more source