scholarly journals L q-solutions to the Cosserat spectrum in bounded and exterior domains

Analysis ◽  
2006 ◽  
Vol 26 (1) ◽  
Author(s):  
Stephan Weyers
Keyword(s):  
Accumulation Point ◽  
Exterior Domains ◽  
Finite Multiplicity ◽  
Cosserat Spectrum ◽  
Infinite Multiplicity

SummaryIfλ = 1 is an eigenvalue of infinite multiplicity and λ = 2 is an accumulation point of eigenvalues of finite multiplicity. For the

A New Class of Maximal Triangular Algebras

2018 ◽  
Vol 61 (4) ◽  
pp. 909-931
Author(s):  
John Lindsay Orr
Keyword(s):  
Finite Multiplicity ◽  
Asymptotic Structure ◽  
C Algebras ◽  
New Class ◽  
Related Family ◽  
Infinite Multiplicity ◽  
Triangular Algebras

AbstractTriangular algebras, and maximal triangular algebras in particular, have been objects of interest for over 50 years. Rich families of examples have been studied in the context of many w*- and C*-algebras, but there remains a dearth of concrete examples in $B({\cal H})$. In previous work, we described a family of maximal triangular algebras of finite multiplicity. Here, we investigate a related family of maximal triangular algebras with infinite multiplicity, and unearth a new asymptotic structure exhibited by these algebras.

A note on nonmultidimensional superstable theories

1985 ◽  
Vol 50 (4) ◽  
pp. 1020-1024 ◽  
Author(s):  
Anand Pillay ◽  
Charles Steinhorn
Keyword(s):  
Stability Theory ◽  
Saturated Model ◽  
Sufficient Condition ◽  
Finite Multiplicity ◽  
Superstable Theory ◽  
Superstable Theories ◽  
Infinite Multiplicity ◽  
Countable Structure

In this paper we prove that if T is the complete elementary diagram of a countable structure and is a theory as in the title, then Vaught's conjecture holds for T. This result is Theorem 7, below. In the process of establishing this proposition, in Theorem 3 we give a sufficient condition for a superstable theory having only countably many types without parameters to be ω-stable. Familiarity with the rudiments of stability theory, as presented in [3] and [4], will be supposed throughout. The notation used is, by now, standard.We begin by giving a new proof of a lemma due to J. Saffe in [6]. For T stable, recall that the multiplicity of a type p over a set A ⊆ ℳ ⊨ T is the cardinality of the collection of strong types over A extending p.Lemma 1 (Saffe). Let T be stable, A ⊆ ℳ ⊨ T. If t(b̄, A) has infinite multiplicity and t(c̄, A) has finite multiplicity, then t(b̄, A ∪ {c̄}) has infinite multiplicity.Proof. We suppose not and work for a contradiction. Let ‹b̄γ:γ ≤ α›, α ≥ ω, be a list of elements so that t(b̄γ, A) = t(b̄, A) for all γ ≤ α, and st(b̄γ, A) ≠ st(b̄δ, A) for γ ≠ δ. Furthermore, let c̄γ satisfy t(b̄γ∧c̄γ, A) = t(b̄ ∧ c̄, A) for each γ < α.Since t(c̄, A) has finite multiplicity, we may assume for all γ, δ < α. that st(c̄γ, A) = st(c̄δ, A). For each γ < α there is an automorphism fγ of the so-called “monster model” of T (a sufficiently large, saturated model of T) that preserves strong types over A and is such that f(c̄γ) = c̄0.

On the spectrum of the periodic Dirac operator

1981 ◽  
Vol 89 (1-2) ◽  
pp. 55-62 ◽  
Author(s):  
B. J. Harris
Keyword(s):  
Dirac Operator ◽  
Spectral Gap ◽  
Dirac Operators ◽  
Finite Multiplicity ◽  
Infinite Multiplicity ◽  
Periodic Dirac Operator

SynopsisIn an earlier paper we considered periodic Dirac operators and obtained criteria for them to be self-adjoint and for their spectra to be devoid of eigenvalues of finite multiplicity. The question of the existence of eigenvalues of infinite multiplicity was left open. In this article we obtain further criteria for self-adjointness and show that under these conditions periodic Dirac operators do not possess eigenvalues of infinite multiplicity. We also obtain a spectral gap result.

Obstructions for semigroups of partial isometries to be self-adjoint

2016 ◽  
Vol 161 (1) ◽  
pp. 107-116
Author(s):  
JANEZ BERNIK ◽  
ALEXEY I. POPOV
Keyword(s):  
Hilbert Space ◽  
Von Neumann Algebra ◽  
Separable Hilbert Space ◽  
Finite Multiplicity ◽  
Partial Isometries ◽  
Von Neumann ◽  
Infinite Multiplicity ◽  
Complex Separable Hilbert Space

AbstractIn this paper we study the following question: given a semigroup ${\mathcal S}$ of partial isometries acting on a complex separable Hilbert space, when does the selfadjoint semigroup ${\mathcal T}$ generated by ${\mathcal S}$ again consist of partial isometries? It has been shown by Bernik, Marcoux, Popov and Radjavi that the answer is positive if the von Neumann algebra generated by the initial and final projections corresponding to the members of ${\mathcal S}$ is abelian and has finite multiplicity. In this paper we study the remaining case of when this von Neumann algebra has infinite multiplicity and show that, in a sense, the answer in this case is generically negative.

scholarly journals Global existence of null-form wave equations in exterior domains

2007 ◽  
Vol 256 (3) ◽  
pp. 521-549 ◽  
Author(s):  
Jason Metcalfe ◽  
Christopher D. Sogge
Keyword(s):  
Global Existence ◽  
Wave Equations ◽  
Exterior Domains

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

Stability results for fluids of Oldroyd-B type on exterior domains

2014 ◽  
Vol 55 (9) ◽  
pp. 091505 ◽  
Author(s):  
Matthias Geissert ◽  
Matthias Hieber ◽  
Nguyen Thieu Huy
Keyword(s):  
Exterior Domains ◽  
Stability Results
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