Representing Systems of Dilations and Translations in Symmetric Function Spaces
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DOI: 10.1007/s00041-019-09715-8
Abstract: Let X be an arbitrary separable symmetric function space on [0, 1]. By using a combination of the frame approach and the notion of the multiplicator space $$\mathscr {M}(X)$$ M ( X ) of X with… read more here.
Keywords: space; varlambda varphi; symmetric function; dilations translations ... See more keywords
Popular subsets for Euler’s $$\varphi $$φ-function
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DOI: 10.1007/s00208-018-01802-3
Abstract: Let $$\varphi (n) = \#(\mathbb {Z}/n\mathbb {Z})^{\times }$$φ(n)=#(Z/nZ)× (Euler’s totient function). Let $$\epsilon > 0$$ϵ>0, and let $$\alpha \in (0,1)$$α∈(0,1). We prove that for all $$x > x_0(\epsilon ,\alpha )$$x>x0(ϵ,α) and every subset $$\mathscr {S}$$S… read more here.
Keywords: euler varphi; mathscr; subsets euler; popular subsets ... See more keywords
Light deflection and Gauss–Bonnet theorem: definition of total deflection angle and its applications
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DOI: 10.1007/s10714-018-2368-2
Abstract: In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild–de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle $$\alpha $$α… read more here.
Keywords: deflection; total deflection; geometry; mathscr ... See more keywords
New Subclasses of the Class of ℋ$$ \mathrm{\mathscr{H}} $$-Matrices and Related Bounds for the Inverses
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DOI: 10.1007/s10958-017-3461-x
Abstract: The paper introduces new subclasses, called Pℋ$$ \mathrm{\mathscr{H}} $$N(π) and Pℋ$$ \mathrm{\mathscr{H}} $$QN(π), of (nonsingular) ℋ$$ \mathrm{\mathscr{H}} $$-matrices of order n dependent on a partition π of the index set {1, . . ., n},… read more here.
Keywords: bounds inverses; mathrm mathscr; mathscr matrices; mathscr ... See more keywords
A sufficient condition for that an operator map is of the form of functional calculus
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DOI: 10.1007/s11117-018-0610-5
Abstract: Let $${\mathscr {H}}$$H be a Hilbert space, J be an open interval and $$B_J({\mathscr {H}})$$BJ(H) be the set of all self-adjoint operators on $${\mathscr {H}}$$H with spectra in J. Suppose that $$\phi :B_J({\mathscr {H}})\rightarrow B({\mathscr… read more here.
Keywords: sufficient condition; mathscr; operator map; phi ... See more keywords
Condition Spectrum of Rank One Operators and Preservers of the Condition Spectrum of Skew Product of Operators
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DOI: 10.1007/s11785-020-01028-9
Abstract: Let $${\mathscr {L}}({\mathscr {H}})$$ be the algebra of all bounded linear operators on a complex Hilbert space $${\mathscr {H}}$$ with $$\dim {\mathscr {H}}\ge 3$$ , and let $$\mathscr {A} $$ and $$\mathscr {B}$$ be two… read more here.
Keywords: varepsilon; condition spectrum; rank one; mathscr ... See more keywords
Double Extensions of Restricted Lie (Super)Algebras
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DOI: 10.1007/s40598-020-00149-5
Abstract: A double extension ($\mathscr{D}$ extension) of a Lie (super)algebra $\mathfrak a$ with a non-degenerate invariant symmetric bilinear form $\mathscr{B}$, briefly: a NIS-(super)algebra, is an enlargement of $\mathfrak a$ by means of a central extension and… read more here.
Keywords: lie super; super algebra; restricted lie; mathscr ... See more keywords
From the Ingham–Jessen property to mixed-mean inequalities
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DOI: 10.1016/j.jmaa.2021.124999
Abstract: For every symmetric mean $\mathscr{M} \colon \bigcup_{n=1}^\infty I^n \to I$ (where $I$ an interval) and a nonzero function $W \colon \{1,\dots,n\} \to \mathbb{N} \cup \{0\}$, define an $n$-variable mean by $$\mathscr{M}_W(x):=\mathscr{M}\big(\underbrace{x_1,\dots,x_1}_{W(1)\text{-times}},\dots,\underbrace{x_n,\dots,x_n}_{W(n)\text{-times}}\big) \text{ for }x=(x_1,\dots,x_n) \in… read more here.
Keywords: mixed mean; mathscr big; big mathscr; ingham jessen ... See more keywords
On the semiprimitivity of free skew extensions of rings
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DOI: 10.1016/j.jpaa.2020.106307
Abstract: Let $X$ be a set of noncommuting variables of cardinality $card(X)\geqslant 2$, and ${\mathscr G}=\{\sigma_x\}_{x\in X}$, ${\mathscr D}=\{\delta_x\}_{x\in X}$ be families of automorphisms and skew derivations of the ring $R$. It is proved that if… read more here.
Keywords: skew extensions; skew; extensions rings; mathscr ... See more keywords
Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses
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DOI: 10.1038/s41598-017-01401-3
Abstract: Since the parity-time-($$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$PT-symmetric potentials have been investigated. However, previous studies of $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$PT-symmetric waves were limited to constant diffraction coefficients… read more here.
Keywords: pmb mathscr; mathscr; stable solitons; mathscr pmb ... See more keywords
A Novelty in Blahut-Arimoto Type Algorithms: Optimal Control Over Noisy Communication Channels
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DOI: 10.1109/tvt.2020.2986788
Abstract: A probability-theoretic problem under information constraints for the concept of optimal control over a noisy-memoryless channel is considered. For our Observer-Controller block, i.e., the lossy joint-source-channel-coding (JSCC) scheme, after providing the relative mathematical expressions, we… read more here.
Keywords: inline formula; tex math; mathscr mathscr; mathscr ... See more keywords