scholarly journals Spectral multiplier theorems of Euclidean type on new classes of two-step stratified groups

2014 ◽  
Vol 109 (5) ◽  
pp. 1229-1263 ◽  
Author(s):  
Alessio Martini ◽  
Detlef Müller
Keyword(s):  
Spectral Multiplier ◽  
Stratified Groups ◽  
Multiplier Theorems ◽  
Spectral Multiplier Theorems ◽  
Euclidean Type

scholarly journals Restriction and spectral multiplier theorems on asymptotically conic manifolds

2013 ◽  
Vol 6 (4) ◽  
pp. 893-950 ◽  
Author(s):  
Colin Guillarmou ◽  
Andrew Hassell ◽  
Adam Sikora
Keyword(s):  
Spectral Multiplier ◽  
Multiplier Theorems ◽  
Spectral Multiplier Theorems

scholarly journals Remarks on L p -limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems

2018 ◽  
Vol 30 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Shanlin Huang ◽  
Xiaohua Yao ◽  
Quan Zheng
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Spectral Condition ◽  
Multiplier Theorem ◽  
Spectral Multiplier ◽  
Limiting Absorption Principle ◽  
Riesz Operators ◽  
Multiplier Theorems ◽  
Spectral Multiplier Theorems ◽  
Formula Type

Abstract This paper comprises two parts. We first investigate an {L^{p}} -type of limiting absorption principle for Schrödinger operators {H=-\Delta+V} on {\mathbb{R}^{n}} ( {n\geq 3} ), i.e., we prove the ϵ-uniform {L^{{2(n+1)}/({n+3})}} – {L^{{2(n+1)}/({n-1})}} -estimates of the resolvent {(H-\lambda\pm i\epsilon)^{-1}} for all {\lambda>0} under the assumptions that the potential V belongs to some integrable spaces and a spectral condition of H at zero is satisfied. As applications, we establish a sharp Hörmander-type spectral multiplier theorem associated with Schrödinger operators H and deduce {L^{p}} -bounds of the corresponding Bochner–Riesz operators. Next, we consider the fractional Schrödinger operator {H=(-\Delta)^{\alpha}+V} ( {0<2\alpha<n} ) and prove a uniform Hardy–Littlewood–Sobolev inequality for {(-\Delta)^{\alpha}} , which generalizes the corresponding result of Kenig–Ruiz–Sogge [20].

scholarly journals Spectral multiplier theorems and averaged R-boundedness

2017 ◽  
Vol 94 (2) ◽  
pp. 260-296 ◽  
Author(s):  
Christoph Kriegler ◽  
Lutz Weis
Keyword(s):  
Spectral Multiplier ◽  
Multiplier Theorems ◽  
Spectral Multiplier Theorems

scholarly journals Fundamental solutions for non-divergence form operators on stratified groups

2003 ◽  
Vol 356 (7) ◽  
pp. 2709-2737 ◽  
Author(s):  
Andrea Bonfiglioli ◽  
Ermanno Lanconelli ◽  
Francesco Uguzzoni
Keyword(s):  
Fundamental Solutions ◽  
Divergence Form ◽  
Stratified Groups

scholarly journals Classification of Symmetric Special Biserial Algebras With At Most One Non-Uniserial Indecomposable Projective

2015 ◽  
Vol 58 (3) ◽  
pp. 739-767 ◽  
Author(s):  
Nicole Snashall ◽  
Rachel Taillefer
Keyword(s):  
Natural Generalization ◽  
Stable Equivalence ◽  
Symmetric Algebras ◽  
Special Biserial Algebras ◽  
Weakly Symmetric ◽  
Dihedral Type ◽  
Indecomposable Projective Module ◽  
Algebras Of Dihedral Type ◽  
Euclidean Type

AbstractWe consider a natural generalization of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and relations, then classify them up to derived equivalence and up to stable equivalence of Morita type. This includes the weakly symmetric algebras of Euclidean type n, as studied by Bocian et al., as well as some algebras of dihedral type.

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