Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Restriction estimates, sharp spectral multipliers and endpoint estimates
  for Bochner-Riesz means   We consider abstract non-negative self-adjoint operators on $L^2(X)$ which
satisfy the finite speed propagation property for the corresponding wave
equation. For such operators we introduce a restriction type condition which in
the case of the standard Laplace operator is equivalent to $(p,2)$ restriction
estimate of Stein and Tomas. Next we show that in the considered abstract
setting our restriction type condition implies sharp spectral multipliers and
endpoint estimates for the Bochner-Riesz summability. We also observe that this
restriction estimate holds for operators satisfying dispersive or Strichartz
estimates. We obtain new spectral multiplier results for several second order
differential operators and recover some known results. Our examples include
Schr\"odinger operators with inverse square potentials on $\RR^n$, the harmonic
oscillator, elliptic operators on compact manifolds and Schr\"odinger operators
on asymptotically conic manifolds.

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The categories of this paper are: nlin
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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci