Tagged Questions

20 views

Relationship between eigenvalues of differential operator and eigenvalues of its adjoint operator.

I am considering $L\phi = -\triangle \phi + u \cdot \nabla \phi$ and its "adjoint" operator $L^* \phi = -\triangle \phi - \nabla \cdot (\phi u)$ on a bounded domain $\Omega \subseteq \mathbb{R}^n$. ...
54 views

Real Analysis and dynamics

I am looking for a textbook or similar resource that addresses the content in a rigorous graduate course in real analysis(at the level of Rudin/Royden) with the following criteria: No hand waving - ...
16 views

What is the convergence criterion for linear fixed-point iteration in Banach space?

Consider an iterative process of the form $x^{n+1}=A x^n + b$. When $A$ is a linear operator in $\mathbb R^n$ then the criterion of convergence is $\rho(A)<1$, where $\rho(A)$ is spectral radius of ...
32 views

Riesz Representation Theorem

I am unfamiliar with Quantum Mechanics and all that stuff. I have recently studied Riesz Representation Theorem , I got to know that it justifies ket and the bra notation. Can anyone please give an ...
32 views

uniform equivalence to unit vector basis of $\ell_p$

Let $(e_n)$ be the unit vector basis of $\ell_p$, $1\leq p<\infty$. It is well-known that if $(x_n)\subset\ell_p$ is seminormalized and weakly null then it contains a subsequence equivalent to ...
85 views

Any good, undergraduate level introductions to Functional Analysis?

In my lower division math classes, my instructors referenced functional analysis as essentially the extension of linear algebra to infinite dimensional vector spaces along with some real analysis. As ...
18 views

39 views

Reference for Codimension in Infinite Dimensional Normed vector spaces

There are a couple identities I would like to use related to the codimension and its relationship to the annihilator; some of these seem to be true for all normed vector spaces, and others seem only ...
225 views

Spectral theorem for unbounded self-adjoint operators on REAL Hilbert spaces

In all books that I have checked the spectral theorem (every self-adjoint operator on a Hilbert space is unitary equivalent to a multiplication operator on some $L_2(\mu)$) is only stated for complex ...
27 views

Cross Product Algebras references

Can someone give some references to introductory books or online notes about group algebras and cross-product algebras ? I've already searched on Google (but only for some online notes). The purpose ...
30 views

Various Definitions of Direct Integrals

The Wikipedia article on Direct Integrals gives the following remark on the definition (of the direct integral of Hilbert spaces): This definition is apparently more restrictive than the one given ...
82 views

Reference for Dual Banach Algebras

Can anyone suggest a good reference book to learn about dual Banach algebras? I they come up a lot in things I read but I rarely see more than just an on the fly definition, but not much ...
28 views

Why is the n-fold tensor product of S(R) dense S(Rn) [duplicate]

I need a reference request for the following fact: Every Schwartz function on $\mathbb{R}^n$ is the limit of a series of elements $$(x_1, \dots, x_n) \rightarrow h_1(x_1) \cdots h_n(x_n),$$ where ...
52 views

A question about extensions of Markov semigroups

I've cross-posted this to MO, if a reply appears on that post I'll update this one. Suppose that $\{T(t)\}_{t\geq 0}$ is a Markov semigroup on the space of continuous bounded functions defined on ...
24 views

Gaussian Smoothing Error and “Hard Analysis” Bounds

Let $p \in (0,\infty)$. Consider a function $f \in L^p([0,1])$, and let $$\phi_\epsilon(x) = \frac{\exp(-x^2/2\epsilon^2)}{\sqrt{2\pi\epsilon^2}}$$ denote a $0$-mean Gaussian of variance $\epsilon$ ...
29 views

nonsurjectivity of Banach-Stone theorem

Currently I'm studying the extension of Banach-Stone theorem using this book. There is one section about the removal of surjectivity of the isometric isomorphism between the two function spaces $C(K)$ ...
174 views

C* Algebra textbook recommendation

I have read the first two chapters from Analysis Now and the chapter on C* algebras (chptr 8?). I'm taking a course on C* algebras in the spring and am currently overwhelmed with the choices. I'd ...