Complex Powers of an Elliptic Operator

In summary, the conversation is about a paper written by R.T. Seeley that is cited in multiple papers but cannot be found. The citation for the paper is provided and a suggestion is made to try the CERN document server. However, the paper may only be available in hard copy and it is recommended to contact a library for assistance in obtaining it.
  • #1
unchained1978
93
0
There is a paper written by R.T. Seeley in the Proceedings of Symposia Pure Mathematics that I've seen cited by several papers I've been reading, but I can't find it anywhere. The citation given is
R. SEELEY, Complex Powers of an Elliptic Operator, “Singular Integrals (Proc.
Symp. Pure Math., Chicago, 1966),” 288-307, Amer. Math. Sot., Providence, R. I.,
1967.

If anyone at all could help me find it I would greatly appreciate it.
 
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  • #3
Thanks, although it doesn't look like I can access that paper from here.
 
  • #4
Unfortunately I'm only aware of hard copies of this paper (in the Proceedings book referenced), and I've also been looking for it. If you contact a library which has the book they should be willing to scan it for you.
 
  • #5


I understand the importance of being able to access and reference reliable sources in our research. In regards to the paper written by R.T. Seeley on complex powers of an elliptic operator, I would suggest checking with your university or local library to see if they have a physical or digital copy of the Proceedings of Symposia Pure Mathematics from 1966. You can also try reaching out to the American Mathematical Society to see if they have any resources or archives that may contain the paper. Additionally, there are online databases such as JSTOR or Google Scholar that may have the paper available for purchase or download. I hope this helps in your search and good luck with your research.
 

Related to Complex Powers of an Elliptic Operator

1. What is an elliptic operator?

An elliptic operator is a type of differential operator that occurs frequently in mathematics and physics. It is a linear operator that takes a function as its input and produces another function as its output. It is called "elliptic" because it is characterized by a property known as elliptic regularity, which means that solutions to the operator's equations are smooth and well-behaved.

2. What are complex powers of an elliptic operator?

Complex powers of an elliptic operator are a family of operators that are defined by taking the original elliptic operator and raising it to a complex power. This means that the resulting operator is still linear, but it operates on functions in a different way, producing a different type of output. Complex powers of an elliptic operator are useful for solving certain types of differential equations and have applications in various areas of mathematics and physics.

3. How do complex powers of an elliptic operator relate to spectral theory?

Complex powers of an elliptic operator are closely related to spectral theory, which is the study of the eigenvalues and eigenvectors of linear operators. In particular, the complex powers of an elliptic operator can be expressed in terms of its spectral decomposition, which is a way of breaking the operator down into simpler components. This connection to spectral theory allows for a better understanding of the behavior and properties of complex powers of an elliptic operator.

4. What are some applications of complex powers of an elliptic operator?

Complex powers of an elliptic operator have numerous applications in mathematics and physics. They are used in the study of partial differential equations, where they can help in finding solutions to certain types of equations. They also have applications in quantum field theory, where they are used to describe the behavior of quantum systems. Additionally, complex powers of an elliptic operator have been used in the study of geometry and topology, particularly in relation to the Riemann zeta function and the Selberg trace formula.

5. What are some open questions or areas of research related to complex powers of an elliptic operator?

While complex powers of an elliptic operator have been studied extensively, there are still many open questions and areas of research related to them. For example, there is ongoing research on the behavior of complex powers of an elliptic operator when the underlying manifold is non-compact. There are also connections to the theory of modular forms and automorphic forms that are still being explored. Additionally, there is ongoing work on the properties of complex powers of an elliptic operator in relation to other types of operators, such as pseudodifferential operators, and their applications in different areas of mathematics and physics.

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