I'm trying to work out a solution to a differential equation whose solutions are the banach space-valued functions on [0,/infty), that is f € C(R+, X). where X is the Banach space of scalar-valued functions. I am trying to prove its weak solution via lax milgram theorem. But to apply lax milgram, I need my vector space to be a Hilbert space. Also, if someone has the book "Banach and Hilbert space of vector-valued functions: their general theory and applications to holomorphy", please post it here, I can't find its free pdf.
Hi everyone, I'm trying to prove that any self-adjoint linear operator A:H->H on a Hilbert space is bounded. I figured the best way would be to show that A is continuous, and therefore bounded. I followed a path of the form:
take x,y close to eachother.
|A(x-y)|^2 = <A(x-y),A(x-y)> = <(x-y),(A^2)(x-y)> <= |x-y||A^2(x-y)|
But this didn't get me anywhere. Any tips would be appreciated
Hey r/learnmath! I have a question on functional analysis! Given is the complex sequence space l^(2)_C. (I will denote it l^(2) from now on). I have to show that a linear, bounded operator A that maps from l^(2) to l^(2) with a finite dimensional range also has an adjoint with a finite dimensional range.
My first thought was this: If I take any sequence a = (a1, a2, a3, ...) from l^(2) and plug it into A (which has finite dimensional range), I get a 'deformed' version of each entry of the sequence: A(a) = (b1, b2, ..., bn, 0, 0, 0,...). If I then work out the requirement for A^(*) (A(a), b) = (a, A^(*)(b)) it is easy to find that the range of the adjoint of A must also be finite dimensional and I am done.
But what if A is the projection of some vector on a infinitely long other vector in l^(2)? Then I still have a finite dimensional range. I think there are more exceptions to the finite operator A just being zeros from some point on, and therefore I would like to give a more general proof. I think there must be some sort of connection between the ranges en nullspaces of A and A^(*) but I can't really grasp it unfortunately. I hope the problem is a bit clear any help would be greatly appreciated!
I only know that ||T|| = ||T* || but this equality could hold for a smaller subspace D(T*) of H. Could someone clarify this? Thanks!
Should I play all of the routes or only certain ones because I've heard that only some are good
Why does Makise's father forgive her in her story, but kill her in the world war three world line?
Also, why is the time leap machine never stolen or guarded, whilst they kidnap Daru and kill Mayuri at the lab? Would it not make more sense to steal it as well? Sorry if the answers obvious, Im ADD and I had a hard time paying attention to the story.
In kurisu route kurisu used time leap and went to okabe to cheer up him saying "you're mad scientist right? of course!" right? Then Why reading steiner didn't work? okabe that didn't get any help by anybody will experience reading steiner to okabe that get help by kurisu. Or It's because okabe did time leap?
I'm on my first read of the og steins gate vn and i'm loving how much more detailed and complex it is compared to the anime and this is ignoring the possible routes (though obviously only route i personally enjoy most is kurisu's/true given despite the other routes having nice moment for those characters it's still sorta, bad ends considering). I'll read the vn after the og but sg 0 is basically okabe gives up on saving kurisu then is basically explaining ww3 and what made him change his mind and realise what to do so hence what happens in 0 is sorta gone from the minds of the characters beyond okabe himself given the og sg ending is where it ends up? And i'm curious what Linear Bounded Phenogram and My darling embrace are. Are they canon additions and if so when are they set and are they more calm additions to the story?
So I played Steins;Gate Linear Bounded Phenogram Chapter 1 and got a question.
To exclude that I completely misunderstood the plot, here's a short summary of what I think the plot (at least the needed part for my problem) is:
It diverges from the 'true story' at the point where Okabe asked Kurisu for help, so he made a dozen of Time Leaps seeing Mayuri die and then just accepts it as inevitible.
Meaning none of the D-Mails got canceled.
But then why is Lukako referred as a guy (or was I just to tired last night and don't remember correctly?)?
Coz when no D-Mail got canceled, Lukako should still be a girl, shouldn't he?
I know that it plays on multiple worldlines that weren't shown in Steins;Gate or Steins;Gate 0, but do we know if what happened on these worldlines is canon?
I only have ripped the most zoomed out sprites but I figured since there's no public rip I could find that I should post mine here. I don't think it's spoiler-y but I'm still tagging the post for good measure. LMK if the link is broken or anything.
https://drive.google.com/drive/folders/1FIsezjfnqg7_bkbfTDKF7Tt5t1Nbc28m?usp=sharing
Hello there, it's my first post on this subreddit, I hope to have fun and I have a question regarding the continuity between those two titles: In what way should I jump between the two games to maintain a sense of continuity? I've seen there are dates on the phone I can follow, but has anyone already charted a path of sorts?
Hello Statistics experts,
I have a question regarding the use of a linear regression. My DV is a score of 0-100 (%). I know that a linear regression can not be used to predict the values because it might predict outside of the bounds of this DV (for example 110%). So I cannot predict. But can I use the p-levels of the regression outcome for my independent variables to determine a statistical correlation? For example can I still use the regression to say a certain independent variable has an effect on the DV (just not by how much or which direction)? Or is that also out of the question?
The DV is often times among the upper ranges of the bounded values. So 50-100. When I rescale my data, the same independent variables are p < 0.05.
I hope you guys can help me. And if someone knows the right test to use I would gladly hear it as well. I have been reading about Beta Regression, but I cant find a tutorial anywhere on how to use and interpret that. I need a test to show me the statistical relationship between my performance percentage/proportion DV and 3 independent variables (average management style, average risk allocation and number of applicants.
Thank you so much for helping me.
So I am playing steins gate linear bounded phenogram and at the end of the caged bird sings, >!daru and Yuki are saved by Suzuha, but what I want to know is that in an alternate timeline where Suzuha was not born and therefore was not present at the bomb scene and was not able to save them. how did daru and Yuki survive to allow them to have Suzuha in the future.!<
Kurisu also addressed the paradox and says that there is a chance that this could mean that Suzuha is not >!daru's daughter!< in this timeline, but I don't think it's true.
I Would really appreciate it if someone has an answer.
Hey guys, i was trying to purchase the VN Linear Bounded Phenogram in Steam becuase it has a discount, the problem here is that it only comes in a bundle with SG Elite, so i wanted to know if you can only purchase it by buying the bundle, cause i really dont want Elite, i already have the normal SG.
Do you know something about this?
Thank you btw
So I've started reading Phenogram, but the first route with Okabe taking on the role of a weird super hero is not my cup of tea in terms of tone and it feels a bit pointless to be honest. I wonder, is Phenogram just light hearted fan service like that route or is there anything worth reading aside from comedy and fan service? Something more serious and... "profound".
There are some cute looking CG's in this, I really want to play suzuha's storyline and stuff but I will also have to buy steins gate elite to get it in my country.. Is it worth it ? ive already played my darlings embrace and LOVED IT
Hey guys! I've been studying with the problems from my textbook and have been stuck for quite a while now. The problem asks to prove that if H is a real Hilbert space and T linear operator on H such that (Tx,x)>=0 for all x in H, where (-,-) denotes the inner product. I found the same question on Stack Exchange (https://math.stackexchange.com/questions/803293/show-that-t-is-continuous-with-langle-x-tx-rangle-geq-0?noredirect=1&lq=1), where somebody says that the problem is a special case of a more general theorem for Banach spaces (https://math.stackexchange.com/questions/216858/positive-operator-is-bounded?noredirect=1&lq=1) and mentions the Riesz Representation Theorem. I understand the proof for Banach spaces, what I don't get is how one would use the boundedness of A (using the notation of the second question) to conclude that T is bounded. Any hints are appreciated! Thanks!
