Can anyone suggest some good books/online notes on (real) analytic maps between Banach spaces? I am looking for the basic definitions and the implicit function theorem in this setting. Thanks!
2026-03-30 04:00:15.1774843215
Books/online notes for analytic maps in Banach spaces
98 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in DERIVATIVES
- Derivative of $ \sqrt x + sinx $
- Second directional derivative of a scaler in polar coordinate
- A problem on mathematical analysis.
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Holding intermediate variables constant in partial derivative chain rule
- How would I simplify this fraction easily?
- Why is the derivative of a vector in polar form the cross product?
- Proving smoothness for a sequence of functions.
- Gradient and Hessian of quadratic form
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in BANACH-SPACES
- Problem 1.70 of Megginson's "An Introduction to Banach Space Theory"
- Is the cartesian product of two Hilbert spaces a Hilbert space?
- Why is $\lambda\mapsto(\lambda\textbf{1}-T)^{-1}$ analytic on $\rho(T)$?
- Is ${C}[0,1],\Bbb{R}$ homeomorphic to any $\Bbb{R^n}$, for an integer $n$?
- Identify $\operatorname{co}(\{e_n:n\in\mathbb N\})$ and $\overline{\operatorname{co}}(\{e_n : n\in\mathbb N\})$ in $c_0$ and $\ell^p$
- Theorem 1.7.9 of Megginson: Completeness is a three-space property.
- A weakly open subset of the unit ball of the Read's space $R$ (an infinite-dimensional Banach space) is unbounded.
- Separability of differentiable functions
- Showing $u_{\lambda}(x):= \left(\frac{\lambda}{{\lambda}^{2}+|x|^2}\right)^{\frac{n-2}{2}}$ is not sequentially compact in $L^{2^{*}}$
- Proving that a composition of bounded operator and trace class operator is trace class
Related Questions in ANALYTIC-FUNCTIONS
- Confusion about Mean Value Theorem stated in a textbook
- A question about real-analytic functions vanishing on an open set
- Prove $f$ is a polynomial if the $n$th derivative vanishes
- Show $\not\exists$ $f\in O(\mathbb{C})$ holomorphic such that $f(z)=\overline{z}$ when $|z|=1$.
- Riemann Mapping and Friends in a Vertical Strip
- How to prove that a complex function is not analytic in a rectangle?
- Prove or disprove that every Holomorphic function preserving unboundedness is a polynomial.
- If $f'$ has a zero of order $m$ at $z_0$ then there is $g$ s.t $f(z) - f(z_0) = g(z)^{k+1}$
- Schwarz lemma, inner circle onto inner circle
- Existence of meromorphic root for meromorphic function
Related Questions in IMPLICIT-FUNCTION-THEOREM
- Is there a variant of the implicit function theorem covering a branch of a curve around a singular point?
- Is the Inverse Function Theorem Global?
- $X^2 + X =A$ with $X, A\in \text{Mat}_{2,2} (\mathbb{R})$ . Show that there exists a solution $X$ for a given $A$
- How to see the sign of an entangled PDE
- Help me understand this proof of Implicit Function Theorem on Banach spaces
- Implicit function theorem involving $\cos$ function
- Does this entangled PDE capture the derivative?
- Applying implicit function theorem
- Question involving implicit functions and PDE
- What to do when we can't apply the implicit function theorem?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
I found to be useful these books
Analytic Theory of Global Bifurcation: An Introduction Boris Buffoni and John Toland https://press.princeton.edu/books/hardcover/9780691112985/analytic-theory-of-global-bifurcation
Zeidler, Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems https://link.springer.com/book/9780387909141