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Global functional calculus, lower/upper bounds and evolution equations on manifolds with boundary

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Abstract
Given a smooth manifold M (with or without boundary), in this paper we establish a global functional calculus, without the standard assumption that the operators are classical pseudo-differential operators, and the Garding inequality for global pseudo-differential operators associated with boundary value problems. The analysis that we follow is free of local coordinate systems. Applications of the Garding inequality to the global solvability for a class of evolution problems are also considered.
Keywords
Algebra and Number Theory, Analysis, Ghent Analysis & PDE center, Pseudo-differential operators, Boundary value problems, Global analysis, COMPLEX POWERS, DIFFERENTIAL-OPERATORS, PSEUDODIFFERENTIAL-OPERATORS, INDEX, INEQUALITIES

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MLA
Cardona Sanchez, Duvan, et al. “Global Functional Calculus, Lower/Upper Bounds and Evolution Equations on Manifolds with Boundary.” ADVANCES IN OPERATOR THEORY, vol. 8, no. 3, Springer Science and Business Media LLC, 2023, doi:10.1007/s43036-023-00254-0.
APA
Cardona Sanchez, D., Kumar, V., Ruzhansky, M., & Tokmagambetov, N. (2023). Global functional calculus, lower/upper bounds and evolution equations on manifolds with boundary. ADVANCES IN OPERATOR THEORY, 8(3). https://doi.org/10.1007/s43036-023-00254-0
Chicago author-date
Cardona Sanchez, Duvan, Vishvesh Kumar, Michael Ruzhansky, and Niyaz Tokmagambetov. 2023. “Global Functional Calculus, Lower/Upper Bounds and Evolution Equations on Manifolds with Boundary.” ADVANCES IN OPERATOR THEORY 8 (3). https://doi.org/10.1007/s43036-023-00254-0.
Chicago author-date (all authors)
Cardona Sanchez, Duvan, Vishvesh Kumar, Michael Ruzhansky, and Niyaz Tokmagambetov. 2023. “Global Functional Calculus, Lower/Upper Bounds and Evolution Equations on Manifolds with Boundary.” ADVANCES IN OPERATOR THEORY 8 (3). doi:10.1007/s43036-023-00254-0.
Vancouver
1.
Cardona Sanchez D, Kumar V, Ruzhansky M, Tokmagambetov N. Global functional calculus, lower/upper bounds and evolution equations on manifolds with boundary. ADVANCES IN OPERATOR THEORY. 2023;8(3).
IEEE
[1]
D. Cardona Sanchez, V. Kumar, M. Ruzhansky, and N. Tokmagambetov, “Global functional calculus, lower/upper bounds and evolution equations on manifolds with boundary,” ADVANCES IN OPERATOR THEORY, vol. 8, no. 3, 2023.
@article{01HP4R09NSRNYW8DAPVSX9TZ72,
  abstract     = {{Given a smooth manifold M (with or without boundary), in this paper we establish a global functional calculus, without the standard assumption that the operators are classical pseudo-differential operators, and the Garding inequality for global pseudo-differential operators associated with boundary value problems. The analysis that we follow is free of local coordinate systems. Applications of the Garding inequality to the global solvability for a class of evolution problems are also considered.}},
  articleno    = {{50}},
  author       = {{Cardona Sanchez, Duvan and Kumar, Vishvesh and Ruzhansky, Michael and Tokmagambetov, Niyaz}},
  issn         = {{2662-2009}},
  journal      = {{ADVANCES IN OPERATOR THEORY}},
  keywords     = {{Algebra and Number Theory,Analysis,Ghent Analysis & PDE center,Pseudo-differential operators,Boundary value problems,Global analysis,COMPLEX POWERS,DIFFERENTIAL-OPERATORS,PSEUDODIFFERENTIAL-OPERATORS,INDEX,INEQUALITIES}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{47}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{Global functional calculus, lower/upper bounds and evolution equations on manifolds with boundary}},
  url          = {{http://doi.org/10.1007/s43036-023-00254-0}},
  volume       = {{8}},
  year         = {{2023}},
}

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