How Long to Read Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary

How Long Does it Take to Read Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary?

It takes the average reader and 59 minutes to read Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary by Paul Kirk

Assuming a reading speed of 250 words per minute. Learn more

Description

The subject of this memoir is the spectrum of a Dirac-type operator on an odd-dimensional manifold M with boundary and, particularly, how this spectrum varies under an analytic perturbation of the operator. Two types of eigenfunctions are considered: first, those satisfying the ``global boundary conditions'' of Atiyah, Patodi, and Singer and second, those which extend to $L^2$ eigenfunctions on M with an infinite collar attached to its boundary. The unifying idea behind the analysis of these two types of spectra is the notion of certain ``eigenvalue-Lagrangians'' in the symplectic space...

How long is Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary?

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary by Paul Kirk is 58 pages long, and a total of 14,964 words.

This makes it 20% the length of the average book. It also has 18% more words than the average book.

How Long Does it Take to Read Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary Aloud?

The average oral reading speed is 183 words per minute. This means it takes 1 hour and 21 minutes to read Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary aloud.

What Reading Level is Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary?

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary is suitable for students ages 8 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary?

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary by Paul Kirk is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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